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Deck 14: Functions of Two or More Variables
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Question
If 
, find 
.
A)
B)
C)
D)
E)
, find . A)
B)
C)
D)
E)
Question
Evaluate the function at the given values of the independent variables. 
; 
, 
A)
B)
C)
D)
E)
; , A)
B)
C)
D)
E)
Question
Use the function 
to find 
.
A)
B)
C)
D)
E)
to find . A)
B)
C)
D)
E)
Question
Evaluate the function at the given values of the independent variables. 
, 
, 
A)
B)
C)
D)
E)
, , A)
B)
C)
D)
E)
Question
Suppose that a gas satisfies the universal gas law, 
with n equal to 40 moles of the gas and R, the universal gas constant, equal to 0.082054. What is V if 
(kelvins, the units in which temperature is measured on the Kelvin scale) and 
atmosphere? Round your answer to four decimal places.
A)
B)
C)
D)
E)
with n equal to 40 moles of the gas and R, the universal gas constant, equal to 0.082054. What is V if (kelvins, the units in which temperature is measured on the Kelvin scale) and atmosphere? Round your answer to four decimal places. A)
B)
C)
D)
E)
Question
Use the function 
to find 
.
A)
B)
C)
D)
E)
to find . A)
B)
C)
D)
E)
Question
Suppose that if $100,000 is borrowed to purchase a home, then the monthly payment R is a function of the interest rate i (expressed as a percent) and the number of years n before the mortgage is paid, and is given by 
. Find 
and interpret your answer. Round your answer to two decimal places.
A)
The monthly payment for $100,000 borrowed for 50 years at 2.25% interest is $141.51.
B)
The monthly payment for $100,000 borrowed for 50 years at 2.25% interest is $4,265.02.
C)
The monthly payment for $100,000 borrowed for 50 years at 2.25% interest is $277.78.
D)
The monthly payment for $100,000 borrowed for 50 years at 2.25% interest is $3,801.72.
E)
The monthly payment for $100,000 borrowed for 50 years at 2.25% interest is $278.78.
. Find and interpret your answer. Round your answer to two decimal places. A)
The monthly payment for $100,000 borrowed for 50 years at 2.25% interest is $141.51.B)
The monthly payment for $100,000 borrowed for 50 years at 2.25% interest is $4,265.02.C)
The monthly payment for $100,000 borrowed for 50 years at 2.25% interest is $277.78.D)
The monthly payment for $100,000 borrowed for 50 years at 2.25% interest is $3,801.72.E)
The monthly payment for $100,000 borrowed for 50 years at 2.25% interest is $278.78. Question
Evaluate the function 
to find 
.
A)
B)
C)
D)
E)
to find . A)
B)
C)
D)
E)
Question
In economics, the most economical quantity Q of goods (TVs, dresses, gallons of paint, etc.) for a store to order is given by Wilson's lot size formula 
, where K is the cost of placing the order, M is the number of items sold per week, and h is the weekly holding cost for each item (the cost of storage space, utilities, taxes, security, etc.). Find 
.
A) 205
B) 14
C) 580
D) 42,000
E) 1,640
, where K is the cost of placing the order, M is the number of items sold per week, and h is the weekly holding cost for each item (the cost of storage space, utilities, taxes, security, etc.). Find . A) 205
B) 14
C) 580
D) 42,000
E) 1,640
Question
If 
, find 
.
A)
B)
C)
D)
E)
, find . A)
B)
C)
D)
E)
Question
Give the domain of the function 
.
A) domain: all reals x and y with
B) domain: all reals x and y with
C) domain: all reals x and y with
D) domain: all reals x and y with
and 
E) domain: all reals x and y with
. A) domain: all reals x and y with
B) domain: all reals x and y with
C) domain: all reals x and y with
D) domain: all reals x and y with
and E) domain: all reals x and y with
Question
Give the domain of the function 
.
A) domain: all reals with
and 
B) domain: all reals with
C) domain: all reals with
D) domain: all reals with
E) domain: all reals with
and 
. A) domain: all reals with
and B) domain: all reals with
C) domain: all reals with
D) domain: all reals with
E) domain: all reals with
and Question
Evaluate the function at the given values of the independent variables. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
The future value S of an investment earning 7% compounded continuously is a function of the principal P and the length of time t that the principal been invested. It is given by 
. Find the future value of $42,000 invested for 30 years.
A) $45,045.34
B) $343,326.42
C) $300,979.14
D) $8.17
E) $342,979.14
. Find the future value of $42,000 invested for 30 years. A) $45,045.34
B) $343,326.42
C) $300,979.14
D) $8.17
E) $342,979.14
Question
The following table shows the monthly mortgage payment R for a given interest rate 5% as a function of the amount financed A (in thousands of dollars) and the duration of the loan n in years. If 
, use the table to find 
. Round your answer to the nearest cent.
A)
B)
C) 
D) 
E) 
, use the table to find . Round your answer to the nearest cent. A)
B)
C)
D)
E)
Question
There are different models for measuring the effects of high temperature and humidity. One of these is the Summer Simmer Index (S), given by 
, where T is the air temperature (in degrees Fahrenheit) and H is the relative humidity (expressed as a decimal).
In a certain city, the measured temperature and humidity on a given day are:
Maximum:
with 47% humidity
Minimum:
with 78% humidity
Calculate the Summer Simmer Index S for both the maximum and minimum temperatures.
A) maximum,
;
Minimum,
B) maximum,
;
Minimum,
C) maximum,
;
Minimum,
D) maximum,
;
Minimum,
E) maximum,
;
Minimum,
, where T is the air temperature (in degrees Fahrenheit) and H is the relative humidity (expressed as a decimal). In a certain city, the measured temperature and humidity on a given day are:
Maximum:
with 47% humidityMinimum:
with 78% humidity
Calculate the Summer Simmer Index S for both the maximum and minimum temperatures.
A) maximum,
;Minimum,
B) maximum,
;Minimum,
C) maximum,
;Minimum,
D) maximum,
;Minimum,
E) maximum,
;Minimum,
Question
Give the domain of the function 
.
A) domain: all reals p1 and p2 with
B) domain: all reals p1 and p2 with
C) domain: all reals p1 and p2 with
D) domain: all reals p1 and p2 with
E) domain: all reals p1 and p2 with
. A) domain: all reals p1 and p2 with
B) domain: all reals p1 and p2 with
C) domain: all reals p1 and p2 with
D) domain: all reals p1 and p2 with
E) domain: all reals p1 and p2 with
Question
Suppose that the utility function for two goods X and Y is given by 
, and a consumer purchases 2 units of X and 6 units of Y. If the consumer purchases 2 units of Y, how many units of X must be purchased to retain the same level of utility?
A)
B)
C)
D)
E)
, and a consumer purchases 2 units of X and 6 units of Y. If the consumer purchases 2 units of Y, how many units of X must be purchased to retain the same level of utility? A)
B)
C)
D)
E)
Question
Use the function 
to find 
.
A)
B)
C)
D)
E)
to find . A)
B)
C)
D)
E)
Question
Suppose wind and cold temperatures combine to make the air temperature feel colder than it actually is. This combination is reported as wind chill. The following table shows that wind chill temperatures, WC, are a function of wind speed, s, and air temperature, t. If 
, use the table to find 
and interpret the answer.
A)
For a wind speed of 5 mph and air temperature of 
, the wind-chill temperature is 
.
B)
For a wind speed of 5 mph and air temperature of 
, the wind-chill temperature is 
.
C)
For a wind speed of 5 mph and air temperature of 
, the wind-chill temperature is 
.
D)
For a wind speed of 5 mph and air temperature of 
, the wind-chill temperature is 
.
E)
For a wind speed of 5 mph and air temperature of 
, the wind-chill temperature is 
.
, use the table to find and interpret the answer. A)
For a wind speed of 5 mph and air temperature of , the wind-chill temperature is .B)
For a wind speed of 5 mph and air temperature of , the wind-chill temperature is .C)
For a wind speed of 5 mph and air temperature of , the wind-chill temperature is .D)
For a wind speed of 5 mph and air temperature of , the wind-chill temperature is .E)
For a wind speed of 5 mph and air temperature of , the wind-chill temperature is . Question
If 
, find 
.
A)
B)
C)
D)
E)
, find . A)
B)
C)
D)
E)
Question
Find the slope of the tangent in the positive y-direction to the surface 
at 
.
A)
B)
C)
D)
E)
at . A)
B)
C)
D)
E)
Question
The cost per day to society of an epidemic is 
, where C is in dollars, x is the number of people infected on a given day, and y is the number of people who die on a given day. If 18,500 people are infected and 10 people die on a given day, what is the cost to society? Round your answer to the nearest dollar.
A) 
B) 
C)
D) 
E) 
, where C is in dollars, x is the number of people infected on a given day, and y is the number of people who die on a given day. If 18,500 people are infected and 10 people die on a given day, what is the cost to society? Round your answer to the nearest dollar. A)
B)
C)
D)
E)
Question
If 
, find 
.
A)
B)
C)
D)
E)
, find . A)
B)
C)
D)
E)
Question
Suppose an area of land is to be sprayed with two brands of pesticide: x liters of brand 1 and y liters of brand 2. If the number of thousands of insects killed is given by 
. How many insects would be killed if 60 liters of brand 1 and 130 liters of brand 2 were used? Round your answer to the nearest integer.
A) 
insects
B) 
insects
C) 
insects
D)
insects
E) 
insects
. How many insects would be killed if 60 liters of brand 1 and 130 liters of brand 2 were used? Round your answer to the nearest integer. A)
insectsB)
insectsC)
insectsD)
insectsE)
insects Question
If 
find 
and 
.
A)
B)
C)
D)
E)
find and . A)
B)
C)
D)
E)
Question
If 
, find 
.
A)
B)
C)
D)
E)
, find . A)
B)
C)
D)
E)
Question
Suppose that an indifference curve for two goods, X and Y, has the equation 
. If 30 units of X are purchased, how many units of Y must be purchased to remain on this indifference curve?
A)
units of Y.
B) 57,600 units of Y.
C) 64 units of Y.
D) 87 units of Y.
E) 101 units of Y.
. If 30 units of X are purchased, how many units of Y must be purchased to remain on this indifference curve? A)
units of Y.B) 57,600 units of Y.
C) 64 units of Y.
D) 87 units of Y.
E) 101 units of Y.
Question
If 
, find 
.
A)
B)
C)
D)
E)
, find .A)
B)
C)
D)
E)
Question
If 
, find 
.
A)
B)
C)
D)
E)
, find . A)
B)
C)
D)
E)
Question
Suppose that a company's production for Q units of its product is given by the Cobb-Douglas production function 
, where K is dollars of capital investment and L is labor hours. Find Q if K = $8,600 and L = 640 hours. Round your answer to the nearest whole number.
A) 94,327 units
B) 1,225 units
C) 1,017 units
D) 25,732 units
E) 13,440 units
, where K is dollars of capital investment and L is labor hours. Find Q if K = $8,600 and L = 640 hours. Round your answer to the nearest whole number. A) 94,327 units
B) 1,225 units
C) 1,017 units
D) 25,732 units
E) 13,440 units
Question
If 
, find 
.
A)
B)
C)
D)
E)
, find . A)
B)
C)
D)
E)
Question
Find the slope of the tangent in the positive x-direction to the surface 
at the point 
.
A)
B)
C)
D)
E)
at the point .A)
B)
C)
D)
E)
Question
If 
, find 
.
A)
B)
C)
D)
E)
, find . A)
B)
C)
D)
E)
Question
If 
, find 
and 
.
A)
B)
C)
D)
E)
, find and . A)
B)
C)
D)
E)
Question
If 
, find 
and 
.
A)
B)
C)
D)
E)
, find and . A)
B)
C)
D)
E)
Question
If 
, find 
.
A)
B)
C)
D)
E)
, find . A)
B)
C)
D)
E)
Question
If 
, find 
and 
.
A)
B)
C)
D)
E)
, find and . A)
B)
C)
D)
E)
Question
Suppose that the number of units of a good produced z is given by 
, where x is the number of machines working properly and y is the average number of work hours per machine. Find the production for a week in which 9 machines are working properly and the average number of work hours per machine is 35. Round your answer to the nearest whole number.
A) 11,025 units
B) 4,410 units
C) 126 units
D) 1,134 units
E) 17,150 units
, where x is the number of machines working properly and y is the average number of work hours per machine. Find the production for a week in which 9 machines are working properly and the average number of work hours per machine is 35. Round your answer to the nearest whole number. A) 11,025 units
B) 4,410 units
C) 126 units
D) 1,134 units
E) 17,150 units
Question
If 
, find 
and 
.
A)
B)
C)
D)
E)
, find and . A)
B)
C)
D)
E)
Question
If the joint cost function for two products is 
(in dollars). Find the marginal cost with respect to y.
A)
B)
C)
D)
E)
(in dollars). Find the marginal cost with respect to y.A)
B)
C)
D)
E)
Question
Suppose that the joint cost function for two products is 
dollars. Find the marginal cost (function) with respect to x.
A)
B)
C)
D)
E)
dollars. Find the marginal cost (function) with respect to x. A)
B)
C)
D)
E)
Question
If 
, find 
.
A)
B)
C)
D)
E)
, find . A)
B)
C)
D)
E)
Question
If 
is the utility function for goods X and Y, the marginal utility of X is 
and the marginal utility of Y is 
. If 
, find the marginal utility of X and Y.
A)
B)
C)
D)
E)
is the utility function for goods X and Y, the marginal utility of X is and the marginal utility of Y is . If , find the marginal utility of X and Y.A)
B)
C)
D)
E)
Question
Suppose that the output Q (in units) of a certain company is 
, where K is the capital expenditures in thousands of dollars and L is the number of labor hours. Find 
and 
when capital expenditures are $45,000 and the labor hours total 5,400. Round your answers to two decimal places.
A)
B)
C)
D)
E)
, where K is the capital expenditures in thousands of dollars and L is the number of labor hours. Find and when capital expenditures are $45,000 and the labor hours total 5,400. Round your answers to two decimal places. A)
B)
C)
D)
E)
Question
If 
, find 
.
A)
B)
C)
D)
E)
, find . A)
B)
C)
D)
E)
Question
The total cost (in dollars) of producing 1 unit of a product is given by 
, where x represents the cost per pound of raw materials and y represents the hourly rate for labor. The present cost for raw materials is $15 per pound and the present hourly rate for labor is $11. Indicate how to use the cost function C to determine how an increase of $1 per pound for raw materials will affect the total cost. Round your answer to two decimal places.
A)
B)
C)
D)
E)
, where x represents the cost per pound of raw materials and y represents the hourly rate for labor. The present cost for raw materials is $15 per pound and the present hourly rate for labor is $11. Indicate how to use the cost function C to determine how an increase of $1 per pound for raw materials will affect the total cost. Round your answer to two decimal places. A)
B)
C)
D)
E)
Question
If 
, find 
.
A)
B)
C)
D)
E)
, find . A)
B)
C)
D)
E)
Question
Suppose that the joint cost (in dollars) for two products is given by 
, where x represents the quantity of product X produced and y represents the quantity of product Y produced. Find and interpret the marginal cost with respect to y if 6 units of product X and 10 units of product Y are produced.
A) If x remains at 6, the expected change in cost for an 11th unit of y is $32.
B) If x remains at 6, the expected change in cost for an 11th unit of y is $15.
C) If x remains at 6, the expected change in cost for an 11th unit of y is $20.
D) If x remains at 6, the expected change in cost for an 11th unit of y is $36.
E) If x remains at 6, the expected change in cost for an 11th unit of y is $51.
, where x represents the quantity of product X produced and y represents the quantity of product Y produced. Find and interpret the marginal cost with respect to y if 6 units of product X and 10 units of product Y are produced. A) If x remains at 6, the expected change in cost for an 11th unit of y is $32.
B) If x remains at 6, the expected change in cost for an 11th unit of y is $15.
C) If x remains at 6, the expected change in cost for an 11th unit of y is $20.
D) If x remains at 6, the expected change in cost for an 11th unit of y is $36.
E) If x remains at 6, the expected change in cost for an 11th unit of y is $51.
Question
The joint cost (in dollars) for two products is given by 
, where x represents the quantity of product X produced and y represents the quantity of product Y produced. Find the marginal cost with respect to x if 2 units of product X and 9 units of product Y are produced.
A)
B)
C) 
D) 
E) 
, where x represents the quantity of product X produced and y represents the quantity of product Y produced. Find the marginal cost with respect to x if 2 units of product X and 9 units of product Y are produced. A)
B)
C)
D)
E)
Question
If 
, find 
.
A)
B)
C)
D)
E)
, find . A)
B)
C)
D)
E)
Question
If 
, find 
.
A)
B)
C)
D)
E)
, find . A)
B)
C)
D)
E)
Question
The total cost (in dollars) of producing 1 unit of a product is 
, where x is the cost per pound of raw materials and y is the cost per hour of labor. If labor costs are held constant, at what rate will the total cost increase for each increase of $1 per pound in material cost? If material costs are held constant, at what rate will the total cost increase for each $1 per hour increase in labor costs?
A)
B)
C)
D)
E)
, where x is the cost per pound of raw materials and y is the cost per hour of labor. If labor costs are held constant, at what rate will the total cost increase for each increase of $1 per pound in material cost? If material costs are held constant, at what rate will the total cost increase for each $1 per hour increase in labor costs? A)
B)
C)
D)
E)
Question
Suppose that the number of thousands of insects killed by two brands of pesticide is given by 
, where x is the number of liters of Brand X and y is the number of liters of Brand Y. What is the rate of change of insect deaths with respect to the number of liters of Brand X if 100 liters of each brand are currently being used? Round your answer to two decimal places.
A)
B)
C)
D)
E)
, where x is the number of liters of Brand X and y is the number of liters of Brand Y. What is the rate of change of insect deaths with respect to the number of liters of Brand X if 100 liters of each brand are currently being used? Round your answer to two decimal places.A)
B)
C)
D)
E)
Question
In economics, the most economical quantity Q of goods (TVs, dress, gallons of paint, etc.) for a store to order is given by Wilson's lot size formula 
, where K is the cost of placing the order, M is the number of items sold per week, and h is the weekly holding costs for each item (the cost of storage space, utilities, taxes, security, etc.). Calculate 
for 
, 
, and 
. Round your answer to two decimal places.
A) 
B)
C) 
D) 
E) 
, where K is the cost of placing the order, M is the number of items sold per week, and h is the weekly holding costs for each item (the cost of storage space, utilities, taxes, security, etc.). Calculate for , , and . Round your answer to two decimal places.A)
B)
C)
D)
E)
Question
A biologist has conjectured that the weight of a certain lizard in pounds as a function of age A in years and length L in inches is given by 
. If a lizard were to remain 13 inches long as it aged from 4 to 5 years old, then determine how much the lizard's weight would be predicted to increase over that year. Round to three decimal places.
A) 
lbs
B) 
lbs
C) 
lbs
D)
lbs
E) 
lbs
. If a lizard were to remain 13 inches long as it aged from 4 to 5 years old, then determine how much the lizard's weight would be predicted to increase over that year. Round to three decimal places. A)
lbsB)
lbsC)
lbsD)
lbsE)
lbs Question
The cost (in dollars) of manufacturing one item is given by 
, where x is the cost of 1 hour of labor and y is the cost of 1 pound of material. If the hourly cost of labor is $5, and the material costs $2 per pound, what is the cost of manufacturing one of these items?
A)
B)
C)
D)
E)
, where x is the cost of 1 hour of labor and y is the cost of 1 pound of material. If the hourly cost of labor is $5, and the material costs $2 per pound, what is the cost of manufacturing one of these items? A)
B)
C)
D)
E)
Question
Suppose that the total cost of producing 1 unit of a product is given by 
dollars, where x represents the cost per pound of raw materials and y represents the hourly rate for labor. The present cost for raw materials is $11 per pound and the present hourly rate for labor is $24. How will an increase of $1 per hour in labor costs affect the total cost? Round your answer to the nearest cent.
A) The total cost will increase approximately $75.28 if labor costs increase to $25 per hour.
B) The total cost will increase approximately $77.41 if labor costs increase to $25 per hour.
C) The total cost will increase approximately $133.36 if labor costs increase to $25 per hour.
D) The total cost will increase approximately $25.78 if labor costs increase to $25 per hour.
E) The total cost will increase approximately $27.95 if labor costs increase to $25 per hour.
dollars, where x represents the cost per pound of raw materials and y represents the hourly rate for labor. The present cost for raw materials is $11 per pound and the present hourly rate for labor is $24. How will an increase of $1 per hour in labor costs affect the total cost? Round your answer to the nearest cent. A) The total cost will increase approximately $75.28 if labor costs increase to $25 per hour.
B) The total cost will increase approximately $77.41 if labor costs increase to $25 per hour.
C) The total cost will increase approximately $133.36 if labor costs increase to $25 per hour.
D) The total cost will increase approximately $25.78 if labor costs increase to $25 per hour.
E) The total cost will increase approximately $27.95 if labor costs increase to $25 per hour.
Question
Dr. Paul Siple conducted studies testing the effect of wind on the formation of ice at various temperatures and developed the concept of wind chill, which we hear reported during winter weather reports. One form of the formula that meteorologists use to calculate wind chill temperature is 
, where s is wind speed and t is the actual air temperature. Find 
when the temperature is 
and the wind speed is 40 mph. Round your answer to two decimal places.
A)
B)
C)
D)
E)
, where s is wind speed and t is the actual air temperature. Find when the temperature is and the wind speed is 40 mph. Round your answer to two decimal places. A)
B)
C)
D)
E)
Question
If 
, find 
.
A)
B)
C)
D)
E)
, find . A)
B)
C)
D)
E)
Question
Suppose that the production function for a product is 
, where x represents the number of work-hours and y represents the available capital (per week). Find the marginal productivity of x.
A)
B)
C)
D)
E)
, where x represents the number of work-hours and y represents the available capital (per week). Find the marginal productivity of x. A)
B)
C)
D)
E)
Question
Suppose the production function for a product is 
, where x is the capital expenditures and y is the number of work-hours. Find the marginal productivity of y.
A) 
B) 
C) 
D) 
E) 
, where x is the capital expenditures and y is the number of work-hours. Find the marginal productivity of y. A)
B)
C)
D)
E)
Question
Suppose the production function for a product is 
, where x is the capital expenditures and y is the number of work-hours. Find the marginal productivity of x.
A)
B)
C)
D)
E)
, where x is the capital expenditures and y is the number of work-hours. Find the marginal productivity of x. A)
B)
C)
D)
E)
Question
The demand functions for two products are given by 
Where p1 and p2 are in dollars and q1 and q2 are numbers of units.
Find a pair of prices p1 and p2 such that the demands for the products will be equal. Round your answers to the nearest cent.
A)
B) 
C) 
D) 
E)
Where p1 and p2 are in dollars and q1 and q2 are numbers of units.
Find a pair of prices p1 and p2 such that the demands for the products will be equal. Round your answers to the nearest cent.
A)
B)
C)
D)
E)
Question
Test 
for relative maximum and minimum.
A) A relative minimum at (0,0,8)
B) A relative maximum at (0,0,3)
C) A relative maximum at (1,0,8)
D) A relative minimum at (0,0,3)
E) A relative maximum at (3,0,0)
for relative maximum and minimum. A) A relative minimum at (0,0,8)
B) A relative maximum at (0,0,3)
C) A relative maximum at (1,0,8)
D) A relative minimum at (0,0,3)
E) A relative maximum at (3,0,0)
Question
Suppose that the production function for a product is 
, where x represents the number of work hours and y represents the available capital (per week). Find the marginal productivity of y.
A)
B)
C)
D)
E)
, where x represents the number of work hours and y represents the available capital (per week). Find the marginal productivity of y. A)
B)
C)
D)
E)
Question
Suppose that the production function for a product is 
, where x represents the number of work hours per month and y is the number of available machines. Determine the marginal productivity of y.
A)
B)
C)
D)
E)
, where x represents the number of work hours per month and y is the number of available machines. Determine the marginal productivity of y.A)
B)
C)
D)
E)
Question
The demand functions for qA and qB units of two related products, A and B, are given by 
Where pA and pB are in dollars.
Find the marginal demand of qA with respect to pB and the marginal demand of qB with respect to pA. Are the two goods competitive or complementary?
A)
B)
C)
D)
E)
Where pA and pB are in dollars.
Find the marginal demand of qA with respect to pB and the marginal demand of qB with respect to pA. Are the two goods competitive or complementary?
A)
B)
C)
D)
E)
Question
Test 
for relative maximum and minimum.
A) A relative minimum occurs at (1,0,13)
B) A relative maximum occurs at (0,0,13)
C) A relative maximum occurs at (1,0,7)
D) A relative minimum occurs at (0,0,7)
E) A relative maximum occurs at (13,0,0)
for relative maximum and minimum. A) A relative minimum occurs at (1,0,13)
B) A relative maximum occurs at (0,0,13)
C) A relative maximum occurs at (1,0,7)
D) A relative minimum occurs at (0,0,7)
E) A relative maximum occurs at (13,0,0)
Question
Suppose that the number of tons of an agricultural product produced is given by 
, where x is the number of hours of labor and y is the number of acres of the crop. Find the number of tons produced when 
and 
. Round your answer to the nearest number of tons.
A)
tons
B)
tons
C) 
tons
D) 
tons
E) 
tons
, where x is the number of hours of labor and y is the number of acres of the crop. Find the number of tons produced when and . Round your answer to the nearest number of tons. A)
tonsB)
tonsC)
tonsD)
tonsE)
tons Question
The demand functions for two products are given by 
Where p1 and p2 are in dollars and q1 and q2 are numbers of units.
Find the demand for each of the products if the price of the first is
and the price of the second is 
.
A) 
units
units
B)
units 
units
C) 
units 
units
D) 
units 
units
E) 
units 
units
Where p1 and p2 are in dollars and q1 and q2 are numbers of units.
Find the demand for each of the products if the price of the first is
and the price of the second is .A)
units
units
B)
units units C)
units units
D)
units units
E)
units units
Question
Suppose that the joint cost function for two products is 
dollars. Find the marginal cost with respect to y.
A)
B)
C)
D)
E)
dollars. Find the marginal cost with respect to y. A)
B)
C)
D)
E)
Question
Suppose that the number of crates of an agricultural product is given by 
, where x is the number of hours of and y is the number of acres of the crop. Find the marginal productivity of the number of hours of labor when 
and 
.
A) 1,090.15
B) 25.39
C) 845.45
D) 19.04
E) -30.97
, where x is the number of hours of and y is the number of acres of the crop. Find the marginal productivity of the number of hours of labor when and . A) 1,090.15
B) 25.39
C) 845.45
D) 19.04
E) -30.97
Question
The demand functions for qA and qB units of two related products, A and B, are given. 
Where pA and pB are in dollars.
Find the marginal demand of qA with respect to pB and the marginal demand of qB with respect to pA. Are the two goods competitive or complementary?
A)
B)
C)
D)
E)
Where pA and pB are in dollars.
Find the marginal demand of qA with respect to pB and the marginal demand of qB with respect to pA. Are the two goods competitive or complementary?
A)
B)
C)
D)
E)
Question
Suppose that the joint cost function in dollars for two products is 
. Find the marginal cost with respect to y.
A)
B)
C)
D)
E)
. Find the marginal cost with respect to y. A)
B)
C)
D)
E)
Question
Test for relative maximum and minimum. 
A) relative minimum at
B) saddle point at
C) saddle point at
D) relative minimum at
E) saddle point at
A) relative minimum at
B) saddle point at
C) saddle point at
D) relative minimum at
E) saddle point at
Question
Suppose the Cobb-Douglas production function for a company is given by 
, where x is the company's capital investment and y is the size of the labor force (in work-hours). Find the marginal productivity of x. Then, find the marginal productivity of y.
A)
B)
C)
D)
E)
, where x is the company's capital investment and y is the size of the labor force (in work-hours). Find the marginal productivity of x. Then, find the marginal productivity of y. A)
B)
C)
D)
E)
Question
Suppose that the joint cost function for two products is 
dollars. Find the marginal cost with respect to x.
A)
B)
C)
D)
E)
dollars. Find the marginal cost with respect to x. A)
B)
C)
D)
E)
Question
Suppose that the production function for a product is 
, where x represents the number of work hours per month and y is the number of available machines. Determine the marginal productivity of x.
A)
B)
C)
D)
E)
, where x represents the number of work hours per month and y is the number of available machines. Determine the marginal productivity of x. A)
B)
C)
D)
E)
Question
Suppose that the joint cost function for two products is 
dollars. Find the marginal cost with respect to x.
A)
B)
C)
D)
E)
dollars. Find the marginal cost with respect to x. A)
B)
C)
D)
E)
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Deck 14: Functions of Two or More Variables
1
If , find .
A)
B)
C)
D)
E)
, find . A)
B)
C)
D)
E)
2
Evaluate the function at the given values of the independent variables. ; ,
A)
B)
C)
D)
E)
; , A)
B)
C)
D)
E)
3
Use the function to find .
A)
B)
C)
D)
E)
to find . A)
B)
C)
D)
E)
4
Evaluate the function at the given values of the independent variables. , ,
A)
B)
C)
D)
E)
, , A)
B)
C)
D)
E)
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5
Suppose that a gas satisfies the universal gas law, with n equal to 40 moles of the gas and R, the universal gas constant, equal to 0.082054. What is V if (kelvins, the units in which temperature is measured on the Kelvin scale) and atmosphere? Round your answer to four decimal places.
A)
B)
C)
D)
E)
with n equal to 40 moles of the gas and R, the universal gas constant, equal to 0.082054. What is V if (kelvins, the units in which temperature is measured on the Kelvin scale) and atmosphere? Round your answer to four decimal places. A)
B)
C)
D)
E)
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6
Use the function to find .
A)
B)
C)
D)
E)
to find . A)
B)
C)
D)
E)
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7
Suppose that if $100,000 is borrowed to purchase a home, then the monthly payment R is a function of the interest rate i (expressed as a percent) and the number of years n before the mortgage is paid, and is given by . Find and interpret your answer. Round your answer to two decimal places.
A) The monthly payment for $100,000 borrowed for 50 years at 2.25% interest is $141.51.
B) The monthly payment for $100,000 borrowed for 50 years at 2.25% interest is $4,265.02.
C) The monthly payment for $100,000 borrowed for 50 years at 2.25% interest is $277.78.
D) The monthly payment for $100,000 borrowed for 50 years at 2.25% interest is $3,801.72.
E) The monthly payment for $100,000 borrowed for 50 years at 2.25% interest is $278.78.
. Find and interpret your answer. Round your answer to two decimal places. A)
The monthly payment for $100,000 borrowed for 50 years at 2.25% interest is $141.51.B)
The monthly payment for $100,000 borrowed for 50 years at 2.25% interest is $4,265.02.C)
The monthly payment for $100,000 borrowed for 50 years at 2.25% interest is $277.78.D)
The monthly payment for $100,000 borrowed for 50 years at 2.25% interest is $3,801.72.E)
The monthly payment for $100,000 borrowed for 50 years at 2.25% interest is $278.78. Unlock Deck
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8
Evaluate the function to find .
A)
B)
C)
D)
E)
to find . A)
B)
C)
D)
E)
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9
In economics, the most economical quantity Q of goods (TVs, dresses, gallons of paint, etc.) for a store to order is given by Wilson's lot size formula , where K is the cost of placing the order, M is the number of items sold per week, and h is the weekly holding cost for each item (the cost of storage space, utilities, taxes, security, etc.). Find .
A) 205
B) 14
C) 580
D) 42,000
E) 1,640
, where K is the cost of placing the order, M is the number of items sold per week, and h is the weekly holding cost for each item (the cost of storage space, utilities, taxes, security, etc.). Find . A) 205
B) 14
C) 580
D) 42,000
E) 1,640
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10
If , find .
A)
B)
C)
D)
E)
, find . A)
B)
C)
D)
E)
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11
Give the domain of the function .
A) domain: all reals x and y with
B) domain: all reals x and y with
C) domain: all reals x and y with
D) domain: all reals x and y with and
E) domain: all reals x and y with
. A) domain: all reals x and y with
B) domain: all reals x and y with
C) domain: all reals x and y with
D) domain: all reals x and y with
and E) domain: all reals x and y with
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12
Give the domain of the function .
A) domain: all reals with and
B) domain: all reals with
C) domain: all reals with
D) domain: all reals with
E) domain: all reals with and
. A) domain: all reals with
and B) domain: all reals with
C) domain: all reals with
D) domain: all reals with
E) domain: all reals with
and Unlock Deck
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13
Evaluate the function at the given values of the independent variables.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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14
The future value S of an investment earning 7% compounded continuously is a function of the principal P and the length of time t that the principal been invested. It is given by . Find the future value of $42,000 invested for 30 years.
A) $45,045.34
B) $343,326.42
C) $300,979.14
D) $8.17
E) $342,979.14
. Find the future value of $42,000 invested for 30 years. A) $45,045.34
B) $343,326.42
C) $300,979.14
D) $8.17
E) $342,979.14
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15
The following table shows the monthly mortgage payment R for a given interest rate 5% as a function of the amount financed A (in thousands of dollars) and the duration of the loan n in years. If , use the table to find . Round your answer to the nearest cent.
A)
B)
C)
D)
E)
, use the table to find . Round your answer to the nearest cent. A)
B)
C)
D)
E)
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16
There are different models for measuring the effects of high temperature and humidity. One of these is the Summer Simmer Index (S), given by , where T is the air temperature (in degrees Fahrenheit) and H is the relative humidity (expressed as a decimal).
In a certain city, the measured temperature and humidity on a given day are:
Maximum: with 47% humidity
Minimum: with 78% humidity
Calculate the Summer Simmer Index S for both the maximum and minimum temperatures.
A) maximum, ;
Minimum,
B) maximum, ;
Minimum,
C) maximum, ;
Minimum,
D) maximum, ;
Minimum,
E) maximum, ;
Minimum,
, where T is the air temperature (in degrees Fahrenheit) and H is the relative humidity (expressed as a decimal). In a certain city, the measured temperature and humidity on a given day are:
Maximum:
with 47% humidityMinimum:
with 78% humidity
Calculate the Summer Simmer Index S for both the maximum and minimum temperatures.
A) maximum,
;Minimum,
B) maximum,
;Minimum,
C) maximum,
;Minimum,
D) maximum,
;Minimum,
E) maximum,
;Minimum,
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17
Give the domain of the function .
A) domain: all reals p1 and p2 with
B) domain: all reals p1 and p2 with
C) domain: all reals p1 and p2 with
D) domain: all reals p1 and p2 with
E) domain: all reals p1 and p2 with
. A) domain: all reals p1 and p2 with
B) domain: all reals p1 and p2 with
C) domain: all reals p1 and p2 with
D) domain: all reals p1 and p2 with
E) domain: all reals p1 and p2 with
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18
Suppose that the utility function for two goods X and Y is given by , and a consumer purchases 2 units of X and 6 units of Y. If the consumer purchases 2 units of Y, how many units of X must be purchased to retain the same level of utility?
A)
B)
C)
D)
E)
, and a consumer purchases 2 units of X and 6 units of Y. If the consumer purchases 2 units of Y, how many units of X must be purchased to retain the same level of utility? A)
B)
C)
D)
E)
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19
Use the function to find .
A)
B)
C)
D)
E)
to find . A)
B)
C)
D)
E)
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20
Suppose wind and cold temperatures combine to make the air temperature feel colder than it actually is. This combination is reported as wind chill. The following table shows that wind chill temperatures, WC, are a function of wind speed, s, and air temperature, t. If , use the table to find and interpret the answer.
A) For a wind speed of 5 mph and air temperature of , the wind-chill temperature is .
B) For a wind speed of 5 mph and air temperature of , the wind-chill temperature is .
C) For a wind speed of 5 mph and air temperature of , the wind-chill temperature is .
D) For a wind speed of 5 mph and air temperature of , the wind-chill temperature is .
E) For a wind speed of 5 mph and air temperature of , the wind-chill temperature is .
, use the table to find and interpret the answer. A)
For a wind speed of 5 mph and air temperature of , the wind-chill temperature is .B)
For a wind speed of 5 mph and air temperature of , the wind-chill temperature is .C)
For a wind speed of 5 mph and air temperature of , the wind-chill temperature is .D)
For a wind speed of 5 mph and air temperature of , the wind-chill temperature is .E)
For a wind speed of 5 mph and air temperature of , the wind-chill temperature is . Unlock Deck
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21
If , find .
A)
B)
C)
D)
E)
, find . A)
B)
C)
D)
E)
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22
Find the slope of the tangent in the positive y-direction to the surface at .
A)
B)
C)
D)
E)
at . A)
B)
C)
D)
E)
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23
The cost per day to society of an epidemic is , where C is in dollars, x is the number of people infected on a given day, and y is the number of people who die on a given day. If 18,500 people are infected and 10 people die on a given day, what is the cost to society? Round your answer to the nearest dollar.
A)
B)
C)
D)
E)
, where C is in dollars, x is the number of people infected on a given day, and y is the number of people who die on a given day. If 18,500 people are infected and 10 people die on a given day, what is the cost to society? Round your answer to the nearest dollar. A)
B)
C)
D)
E)
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24
If , find .
A)
B)
C)
D)
E)
, find . A)
B)
C)
D)
E)
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25
Suppose an area of land is to be sprayed with two brands of pesticide: x liters of brand 1 and y liters of brand 2. If the number of thousands of insects killed is given by . How many insects would be killed if 60 liters of brand 1 and 130 liters of brand 2 were used? Round your answer to the nearest integer.
A) insects
B) insects
C) insects
D) insects
E) insects
. How many insects would be killed if 60 liters of brand 1 and 130 liters of brand 2 were used? Round your answer to the nearest integer. A)
insectsB)
insectsC)
insectsD)
insectsE)
insects Unlock Deck
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26
If find and .
A)
B)
C)
D)
E)
find and . A)
B)
C)
D)
E)
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27
If , find .
A)
B)
C)
D)
E)
, find . A)
B)
C)
D)
E)
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28
Suppose that an indifference curve for two goods, X and Y, has the equation . If 30 units of X are purchased, how many units of Y must be purchased to remain on this indifference curve?
A) units of Y.
B) 57,600 units of Y.
C) 64 units of Y.
D) 87 units of Y.
E) 101 units of Y.
. If 30 units of X are purchased, how many units of Y must be purchased to remain on this indifference curve? A)
units of Y.B) 57,600 units of Y.
C) 64 units of Y.
D) 87 units of Y.
E) 101 units of Y.
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29
If , find .
A)
B)
C)
D)
E)
, find .A)
B)
C)
D)
E)
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30
If , find .
A)
B)
C)
D)
E)
, find . A)
B)
C)
D)
E)
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31
Suppose that a company's production for Q units of its product is given by the Cobb-Douglas production function , where K is dollars of capital investment and L is labor hours. Find Q if K = $8,600 and L = 640 hours. Round your answer to the nearest whole number.
A) 94,327 units
B) 1,225 units
C) 1,017 units
D) 25,732 units
E) 13,440 units
, where K is dollars of capital investment and L is labor hours. Find Q if K = $8,600 and L = 640 hours. Round your answer to the nearest whole number. A) 94,327 units
B) 1,225 units
C) 1,017 units
D) 25,732 units
E) 13,440 units
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32
If , find .
A)
B)
C)
D)
E)
, find . A)
B)
C)
D)
E)
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33
Find the slope of the tangent in the positive x-direction to the surface at the point .
A)
B)
C)
D)
E)
at the point .A)
B)
C)
D)
E)
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34
If , find .
A)
B)
C)
D)
E)
, find . A)
B)
C)
D)
E)
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35
If , find and .
A)
B)
C)
D)
E)
, find and . A)
B)
C)
D)
E)
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36
If , find and .
A)
B)
C)
D)
E)
, find and . A)
B)
C)
D)
E)
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37
If , find .
A)
B)
C)
D)
E)
, find . A)
B)
C)
D)
E)
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38
If , find and .
A)
B)
C)
D)
E)
, find and . A)
B)
C)
D)
E)
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39
Suppose that the number of units of a good produced z is given by , where x is the number of machines working properly and y is the average number of work hours per machine. Find the production for a week in which 9 machines are working properly and the average number of work hours per machine is 35. Round your answer to the nearest whole number.
A) 11,025 units
B) 4,410 units
C) 126 units
D) 1,134 units
E) 17,150 units
, where x is the number of machines working properly and y is the average number of work hours per machine. Find the production for a week in which 9 machines are working properly and the average number of work hours per machine is 35. Round your answer to the nearest whole number. A) 11,025 units
B) 4,410 units
C) 126 units
D) 1,134 units
E) 17,150 units
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40
If , find and .
A)
B)
C)
D)
E)
, find and . A)
B)
C)
D)
E)
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41
If the joint cost function for two products is (in dollars). Find the marginal cost with respect to y.
A)
B)
C)
D)
E)
(in dollars). Find the marginal cost with respect to y.A)
B)
C)
D)
E)
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42
Suppose that the joint cost function for two products is dollars. Find the marginal cost (function) with respect to x.
A)
B)
C)
D)
E)
dollars. Find the marginal cost (function) with respect to x. A)
B)
C)
D)
E)
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43
If , find .
A)
B)
C)
D)
E)
, find . A)
B)
C)
D)
E)
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44
If is the utility function for goods X and Y, the marginal utility of X is and the marginal utility of Y is . If , find the marginal utility of X and Y.
A)
B)
C)
D)
E)
is the utility function for goods X and Y, the marginal utility of X is and the marginal utility of Y is . If , find the marginal utility of X and Y.A)
B)
C)
D)
E)
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45
Suppose that the output Q (in units) of a certain company is , where K is the capital expenditures in thousands of dollars and L is the number of labor hours. Find and when capital expenditures are $45,000 and the labor hours total 5,400. Round your answers to two decimal places.
A)
B)
C)
D)
E)
, where K is the capital expenditures in thousands of dollars and L is the number of labor hours. Find and when capital expenditures are $45,000 and the labor hours total 5,400. Round your answers to two decimal places. A)
B)
C)
D)
E)
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46
If , find .
A)
B)
C)
D)
E)
, find . A)
B)
C)
D)
E)
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47
The total cost (in dollars) of producing 1 unit of a product is given by , where x represents the cost per pound of raw materials and y represents the hourly rate for labor. The present cost for raw materials is $15 per pound and the present hourly rate for labor is $11. Indicate how to use the cost function C to determine how an increase of $1 per pound for raw materials will affect the total cost. Round your answer to two decimal places.
A)
B)
C)
D)
E)
, where x represents the cost per pound of raw materials and y represents the hourly rate for labor. The present cost for raw materials is $15 per pound and the present hourly rate for labor is $11. Indicate how to use the cost function C to determine how an increase of $1 per pound for raw materials will affect the total cost. Round your answer to two decimal places. A)
B)
C)
D)
E)
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48
If , find .
A)
B)
C)
D)
E)
, find . A)
B)
C)
D)
E)
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49
Suppose that the joint cost (in dollars) for two products is given by , where x represents the quantity of product X produced and y represents the quantity of product Y produced. Find and interpret the marginal cost with respect to y if 6 units of product X and 10 units of product Y are produced.
A) If x remains at 6, the expected change in cost for an 11th unit of y is $32.
B) If x remains at 6, the expected change in cost for an 11th unit of y is $15.
C) If x remains at 6, the expected change in cost for an 11th unit of y is $20.
D) If x remains at 6, the expected change in cost for an 11th unit of y is $36.
E) If x remains at 6, the expected change in cost for an 11th unit of y is $51.
, where x represents the quantity of product X produced and y represents the quantity of product Y produced. Find and interpret the marginal cost with respect to y if 6 units of product X and 10 units of product Y are produced. A) If x remains at 6, the expected change in cost for an 11th unit of y is $32.
B) If x remains at 6, the expected change in cost for an 11th unit of y is $15.
C) If x remains at 6, the expected change in cost for an 11th unit of y is $20.
D) If x remains at 6, the expected change in cost for an 11th unit of y is $36.
E) If x remains at 6, the expected change in cost for an 11th unit of y is $51.
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50
The joint cost (in dollars) for two products is given by , where x represents the quantity of product X produced and y represents the quantity of product Y produced. Find the marginal cost with respect to x if 2 units of product X and 9 units of product Y are produced.
A)
B)
C)
D)
E)
, where x represents the quantity of product X produced and y represents the quantity of product Y produced. Find the marginal cost with respect to x if 2 units of product X and 9 units of product Y are produced. A)
B)
C)
D)
E)
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51
If , find .
A)
B)
C)
D)
E)
, find . A)
B)
C)
D)
E)
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52
If , find .
A)
B)
C)
D)
E)
, find . A)
B)
C)
D)
E)
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53
The total cost (in dollars) of producing 1 unit of a product is , where x is the cost per pound of raw materials and y is the cost per hour of labor. If labor costs are held constant, at what rate will the total cost increase for each increase of $1 per pound in material cost? If material costs are held constant, at what rate will the total cost increase for each $1 per hour increase in labor costs?
A)
B)
C)
D)
E)
, where x is the cost per pound of raw materials and y is the cost per hour of labor. If labor costs are held constant, at what rate will the total cost increase for each increase of $1 per pound in material cost? If material costs are held constant, at what rate will the total cost increase for each $1 per hour increase in labor costs? A)
B)
C)
D)
E)
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54
Suppose that the number of thousands of insects killed by two brands of pesticide is given by , where x is the number of liters of Brand X and y is the number of liters of Brand Y. What is the rate of change of insect deaths with respect to the number of liters of Brand X if 100 liters of each brand are currently being used? Round your answer to two decimal places.
A)
B)
C)
D)
E)
, where x is the number of liters of Brand X and y is the number of liters of Brand Y. What is the rate of change of insect deaths with respect to the number of liters of Brand X if 100 liters of each brand are currently being used? Round your answer to two decimal places.A)
B)
C)
D)
E)
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55
In economics, the most economical quantity Q of goods (TVs, dress, gallons of paint, etc.) for a store to order is given by Wilson's lot size formula , where K is the cost of placing the order, M is the number of items sold per week, and h is the weekly holding costs for each item (the cost of storage space, utilities, taxes, security, etc.). Calculate for , , and . Round your answer to two decimal places.
A)
B)
C)
D)
E)
, where K is the cost of placing the order, M is the number of items sold per week, and h is the weekly holding costs for each item (the cost of storage space, utilities, taxes, security, etc.). Calculate for , , and . Round your answer to two decimal places.A)
B)
C)
D)
E)
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56
A biologist has conjectured that the weight of a certain lizard in pounds as a function of age A in years and length L in inches is given by . If a lizard were to remain 13 inches long as it aged from 4 to 5 years old, then determine how much the lizard's weight would be predicted to increase over that year. Round to three decimal places.
A) lbs
B) lbs
C) lbs
D) lbs
E) lbs
. If a lizard were to remain 13 inches long as it aged from 4 to 5 years old, then determine how much the lizard's weight would be predicted to increase over that year. Round to three decimal places. A)
lbsB)
lbsC)
lbsD)
lbsE)
lbs Unlock Deck
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57
The cost (in dollars) of manufacturing one item is given by , where x is the cost of 1 hour of labor and y is the cost of 1 pound of material. If the hourly cost of labor is $5, and the material costs $2 per pound, what is the cost of manufacturing one of these items?
A)
B)
C)
D)
E)
, where x is the cost of 1 hour of labor and y is the cost of 1 pound of material. If the hourly cost of labor is $5, and the material costs $2 per pound, what is the cost of manufacturing one of these items? A)
B)
C)
D)
E)
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58
Suppose that the total cost of producing 1 unit of a product is given by dollars, where x represents the cost per pound of raw materials and y represents the hourly rate for labor. The present cost for raw materials is $11 per pound and the present hourly rate for labor is $24. How will an increase of $1 per hour in labor costs affect the total cost? Round your answer to the nearest cent.
A) The total cost will increase approximately $75.28 if labor costs increase to $25 per hour.
B) The total cost will increase approximately $77.41 if labor costs increase to $25 per hour.
C) The total cost will increase approximately $133.36 if labor costs increase to $25 per hour.
D) The total cost will increase approximately $25.78 if labor costs increase to $25 per hour.
E) The total cost will increase approximately $27.95 if labor costs increase to $25 per hour.
dollars, where x represents the cost per pound of raw materials and y represents the hourly rate for labor. The present cost for raw materials is $11 per pound and the present hourly rate for labor is $24. How will an increase of $1 per hour in labor costs affect the total cost? Round your answer to the nearest cent. A) The total cost will increase approximately $75.28 if labor costs increase to $25 per hour.
B) The total cost will increase approximately $77.41 if labor costs increase to $25 per hour.
C) The total cost will increase approximately $133.36 if labor costs increase to $25 per hour.
D) The total cost will increase approximately $25.78 if labor costs increase to $25 per hour.
E) The total cost will increase approximately $27.95 if labor costs increase to $25 per hour.
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59
Dr. Paul Siple conducted studies testing the effect of wind on the formation of ice at various temperatures and developed the concept of wind chill, which we hear reported during winter weather reports. One form of the formula that meteorologists use to calculate wind chill temperature is , where s is wind speed and t is the actual air temperature. Find when the temperature is and the wind speed is 40 mph. Round your answer to two decimal places.
A)
B)
C)
D)
E)
, where s is wind speed and t is the actual air temperature. Find when the temperature is and the wind speed is 40 mph. Round your answer to two decimal places. A)
B)
C)
D)
E)
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60
If , find .
A)
B)
C)
D)
E)
, find . A)
B)
C)
D)
E)
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61
Suppose that the production function for a product is , where x represents the number of work-hours and y represents the available capital (per week). Find the marginal productivity of x.
A)
B)
C)
D)
E)
, where x represents the number of work-hours and y represents the available capital (per week). Find the marginal productivity of x. A)
B)
C)
D)
E)
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62
Suppose the production function for a product is , where x is the capital expenditures and y is the number of work-hours. Find the marginal productivity of y.
A)
B)
C)
D)
E)
, where x is the capital expenditures and y is the number of work-hours. Find the marginal productivity of y. A)
B)
C)
D)
E)
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63
Suppose the production function for a product is , where x is the capital expenditures and y is the number of work-hours. Find the marginal productivity of x.
A)
B)
C)
D)
E)
, where x is the capital expenditures and y is the number of work-hours. Find the marginal productivity of x. A)
B)
C)
D)
E)
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64
The demand functions for two products are given by
Where p1 and p2 are in dollars and q1 and q2 are numbers of units.
Find a pair of prices p1 and p2 such that the demands for the products will be equal. Round your answers to the nearest cent.
A)
B)
C)
D)
E)
Where p1 and p2 are in dollars and q1 and q2 are numbers of units.
Find a pair of prices p1 and p2 such that the demands for the products will be equal. Round your answers to the nearest cent.
A)
B)
C)
D)
E)
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65
Test for relative maximum and minimum.
A) A relative minimum at (0,0,8)
B) A relative maximum at (0,0,3)
C) A relative maximum at (1,0,8)
D) A relative minimum at (0,0,3)
E) A relative maximum at (3,0,0)
for relative maximum and minimum. A) A relative minimum at (0,0,8)
B) A relative maximum at (0,0,3)
C) A relative maximum at (1,0,8)
D) A relative minimum at (0,0,3)
E) A relative maximum at (3,0,0)
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66
Suppose that the production function for a product is , where x represents the number of work hours and y represents the available capital (per week). Find the marginal productivity of y.
A)
B)
C)
D)
E)
, where x represents the number of work hours and y represents the available capital (per week). Find the marginal productivity of y. A)
B)
C)
D)
E)
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67
Suppose that the production function for a product is , where x represents the number of work hours per month and y is the number of available machines. Determine the marginal productivity of y.
A)
B)
C)
D)
E)
, where x represents the number of work hours per month and y is the number of available machines. Determine the marginal productivity of y.A)
B)
C)
D)
E)
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68
The demand functions for qA and qB units of two related products, A and B, are given by
Where pA and pB are in dollars.
Find the marginal demand of qA with respect to pB and the marginal demand of qB with respect to pA. Are the two goods competitive or complementary?
A)
B)
C)
D)
E)
Where pA and pB are in dollars.
Find the marginal demand of qA with respect to pB and the marginal demand of qB with respect to pA. Are the two goods competitive or complementary?
A)
B)
C)
D)
E)
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69
Test for relative maximum and minimum.
A) A relative minimum occurs at (1,0,13)
B) A relative maximum occurs at (0,0,13)
C) A relative maximum occurs at (1,0,7)
D) A relative minimum occurs at (0,0,7)
E) A relative maximum occurs at (13,0,0)
for relative maximum and minimum. A) A relative minimum occurs at (1,0,13)
B) A relative maximum occurs at (0,0,13)
C) A relative maximum occurs at (1,0,7)
D) A relative minimum occurs at (0,0,7)
E) A relative maximum occurs at (13,0,0)
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70
Suppose that the number of tons of an agricultural product produced is given by , where x is the number of hours of labor and y is the number of acres of the crop. Find the number of tons produced when and . Round your answer to the nearest number of tons.
A) tons
B) tons
C) tons
D) tons
E) tons
, where x is the number of hours of labor and y is the number of acres of the crop. Find the number of tons produced when and . Round your answer to the nearest number of tons. A)
tonsB)
tonsC)
tonsD)
tonsE)
tons Unlock Deck
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71
The demand functions for two products are given by
Where p1 and p2 are in dollars and q1 and q2 are numbers of units.
Find the demand for each of the products if the price of the first is and the price of the second is .
A) units
units
B) units units
C) units units
D) units units
E) units units
Where p1 and p2 are in dollars and q1 and q2 are numbers of units.
Find the demand for each of the products if the price of the first is
and the price of the second is .A)
units
units
B)
units units C)
units units
D)
units units
E)
units units
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72
Suppose that the joint cost function for two products is dollars. Find the marginal cost with respect to y.
A)
B)
C)
D)
E)
dollars. Find the marginal cost with respect to y. A)
B)
C)
D)
E)
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73
Suppose that the number of crates of an agricultural product is given by , where x is the number of hours of and y is the number of acres of the crop. Find the marginal productivity of the number of hours of labor when and .
A) 1,090.15
B) 25.39
C) 845.45
D) 19.04
E) -30.97
, where x is the number of hours of and y is the number of acres of the crop. Find the marginal productivity of the number of hours of labor when and . A) 1,090.15
B) 25.39
C) 845.45
D) 19.04
E) -30.97
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74
The demand functions for qA and qB units of two related products, A and B, are given.
Where pA and pB are in dollars.
Find the marginal demand of qA with respect to pB and the marginal demand of qB with respect to pA. Are the two goods competitive or complementary?
A)
B)
C)
D)
E)
Where pA and pB are in dollars.
Find the marginal demand of qA with respect to pB and the marginal demand of qB with respect to pA. Are the two goods competitive or complementary?
A)
B)
C)
D)
E)
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75
Suppose that the joint cost function in dollars for two products is . Find the marginal cost with respect to y.
A)
B)
C)
D)
E)
. Find the marginal cost with respect to y. A)
B)
C)
D)
E)
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76
Test for relative maximum and minimum.
A) relative minimum at
B) saddle point at
C) saddle point at
D) relative minimum at
E) saddle point at
A) relative minimum at
B) saddle point at
C) saddle point at
D) relative minimum at
E) saddle point at
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77
Suppose the Cobb-Douglas production function for a company is given by , where x is the company's capital investment and y is the size of the labor force (in work-hours). Find the marginal productivity of x. Then, find the marginal productivity of y.
A)
B)
C)
D)
E)
, where x is the company's capital investment and y is the size of the labor force (in work-hours). Find the marginal productivity of x. Then, find the marginal productivity of y. A)
B)
C)
D)
E)
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78
Suppose that the joint cost function for two products is dollars. Find the marginal cost with respect to x.
A)
B)
C)
D)
E)
dollars. Find the marginal cost with respect to x. A)
B)
C)
D)
E)
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79
Suppose that the production function for a product is , where x represents the number of work hours per month and y is the number of available machines. Determine the marginal productivity of x.
A)
B)
C)
D)
E)
, where x represents the number of work hours per month and y is the number of available machines. Determine the marginal productivity of x. A)
B)
C)
D)
E)
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80
Suppose that the joint cost function for two products is dollars. Find the marginal cost with respect to x.
A)
B)
C)
D)
E)
dollars. Find the marginal cost with respect to x. A)
B)
C)
D)
E)
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