Question 1

Suppose that the joint cost function for two products is   dollars. Find the marginal cost with respect to y. ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)    E

Question 2

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?
​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)    A

Question 3

The following table shows the median age of automobiles and trucks on the road for a certain country. Use linear regression to find the linear equation that is the best fit for the data, with x equal to the number of years past 1980. ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)    E

Question 4

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. ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 5

Test for relative maximum and minimum. ​   ​

Accepted Answer

A)  relative minimum at   
B)  relative maximum at   
C)  relative minimum at   
D)  relative maximum at   
E)  relative minimum at   
A)  relative minimum at   
B)  relative maximum at   
C)  relative minimum at   
D)  relative maximum at   
E)  relative minimum at

Question 6

Suppose that the following table shows the average hourly earnings for full-time production workers in various industries for selected years. Find the linear regression equation for hourly earnings as a function of time (with   representing 1970). Round numerical values in your answer to four decimal places. ​

Accepted Answer

A)    (where x is the number of years after 1970 and y is the average hourly wage) 
B)    (where x is the number of years after 1970 and y is the average hourly wage) 
C)    (where x is the number of years after 1970 and y is the average hourly wage) 
D)    (where x is the number of years after 1970 and y is the average hourly wage) 
E)    (where x is the number of years after 1970 and y is the average hourly wage) 
A)    (where x is the number of years after 1970 and y is the average hourly wage) 
B)    (where x is the number of years after 1970 and y is the average hourly wage) 
C)    (where x is the number of years after 1970 and y is the average hourly wage) 
D)    (where x is the number of years after 1970 and y is the average hourly wage) 
E)    (where x is the number of years after 1970 and y is the average hourly wage)

Question 7

Suppose that the following table shows the average hourly earnings for full-time production workers in various industries for selected years. The linear regression equation for hourly earnings as a function of time is given by   (where x is the number of years after 1970 and y is the average hourly wage). What does this model predict for the average hourly earnings in 2024? Round your answer to two decimal places. ​

Accepted Answer

A)  $42.51 
B)  $327.10 
C)  $43.41 
D)  $326.20 
E)  $325.80 
A)  $42.51 
B)  $327.10 
C)  $43.41 
D)  $326.20 
E)  $325.80

Question 8

If   find   and   . ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 9

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. ​

Accepted 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   . 
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 10

Suppose that the joint cost function for two products is   dollars. Find the marginal cost (function) with respect to x. ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 11

If   , find   . ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 12

Test for relative maximum and minimum. ​   ​

Accepted Answer

A)  relative maximum at   
B)  relative maximum at   
C)  relative minimum at   
D)  relative minimum at   
E)  relative minimum at   
A)  relative maximum at   
B)  relative maximum at   
C)  relative minimum at   
D)  relative minimum at   
E)  relative minimum at

Question 13

A new food is designed to add weight to mature beef cattle. The weight in pounds is given by   , where x is the number of units of the first ingredient and y is the number of units of the second ingredient. How many units of each ingredient will maximize the weight? ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 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. ​

Accepted Answer

A)  $45,045.34 
B)  $343,326.42 
C)  $300,979.14 
D)  $8.17 
E)  $342,979.14 
A)  $45,045.34 
B)  $343,326.42 
C)  $300,979.14 
D)  $8.17 
E)  $342,979.14

Question 15

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? ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 16

If   , find   and   . ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 17

Suppose that the joint cost function for two products is   dollars. Find the marginal cost with respect to x. ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 18

Suppose that x units of one input and y units of a second input result in   units of a product. What is the maximum production? ​

Accepted Answer

A)  1,675 
B)  ​3,081 
C)  ​1,152 
D)  ​1,027 
E)  ​1,425 
A)  1,675 
B)  ​3,081 
C)  ​1,152 
D)  ​1,027 
E)  ​1,425

Question 19

Suppose that the joint cost function for two products is   dollars. Find the marginal cost with respect to x. ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 20

Evaluate the function at the given values of the independent variables. ​   ;   ,   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Suppose that the joint cost function for two products is dollars. Find the marginal cost with respect to y.

The demand functions for q_A and q_B units of two related products, A and B, are given by Where p_A and p_B are in dollars. Find the marginal demand of q_A with respect to p_B and the marginal demand of q_B with respect to p_A. Are the two goods competitive or complementary?

The following table shows the median age of automobiles and trucks on the road for a certain country. Use linear regression to find the linear equation that is the best fit for the data, with x equal to the number of years past 1980.

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.

Test for relative maximum and minimum.

If find and .

Suppose that the joint cost function for two products is dollars. Find the marginal cost (function) with respect to x.

If , find .

Test for relative maximum and minimum.

A new food is designed to add weight to mature beef cattle. The weight in pounds is given by , where x is the number of units of the first ingredient and y is the number of units of the second ingredient. How many units of each ingredient will maximize the weight?

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.

If , find and .

Suppose that the joint cost function for two products is dollars. Find the marginal cost with respect to x.

Suppose that x units of one input and y units of a second input result in units of a product. What is the maximum production?

Suppose that the joint cost function for two products is dollars. Find the marginal cost with respect to x.

Evaluate the function at the given values of the independent variables. ; ,

Linear Equations and Functions

Quadratic and Other Special Functions

Matrices

Inequalities and Linear Programming

Exponential and Logarithmic Functions

Mathematics of Finance

Introduction to Probability

Further Topics in Probability and Data Description

Derivatives

Derivatives

Derivatives Continued

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A: Definite Integrals - Techniques

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Exam 14: Functions of Two or More Variables

Suppose that the joint cost function for two products is dollars. Find the marginal cost with respect to y. ​

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? ​

The following table shows the median age of automobiles and trucks on the road for a certain country. Use linear regression to find the linear equation that is the best fit for the data, with x equal to the number of years past 1980. ​

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. ​

Test for relative maximum and minimum. ​ ​

If find and . ​

Suppose that the joint cost function for two products is dollars. Find the marginal cost (function) with respect to x. ​

If , find . ​

Test for relative maximum and minimum. ​ ​

A new food is designed to add weight to mature beef cattle. The weight in pounds is given by , where x is the number of units of the first ingredient and y is the number of units of the second ingredient. How many units of each ingredient will maximize the weight? ​

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. ​

If , find and . ​

Suppose that the joint cost function for two products is dollars. Find the marginal cost with respect to x. ​

Suppose that x units of one input and y units of a second input result in units of a product. What is the maximum production? ​

Suppose that the joint cost function for two products is dollars. Find the marginal cost with respect to x. ​

Evaluate the function at the given values of the independent variables. ​ ; , ​

Linear Equations and Functions

Quadratic and Other Special Functions

Matrices

Inequalities and Linear Programming

Exponential and Logarithmic Functions

Mathematics of Finance

Introduction to Probability

Further Topics in Probability and Data Description

Derivatives

Derivatives

Derivatives Continued

Indefinite Integrals

Definite Integrals - Techniques

A: Definite Integrals - Techniques

Algebraic Concepts 2

Algebraic Concepts 3

Algebraic Concepts 4

Algebraic Concepts 5

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Suppose that the joint cost function for two products is dollars. Find the marginal cost with respect to y.

The demand functions for q_A and q_B units of two related products, A and B, are given by Where p_A and p_B are in dollars. Find the marginal demand of q_A with respect to p_B and the marginal demand of q_B with respect to p_A. Are the two goods competitive or complementary?

The following table shows the median age of automobiles and trucks on the road for a certain country. Use linear regression to find the linear equation that is the best fit for the data, with x equal to the number of years past 1980.

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.

Test for relative maximum and minimum.

If find and .

Suppose that the joint cost function for two products is dollars. Find the marginal cost (function) with respect to x.

If , find .

Test for relative maximum and minimum.

A new food is designed to add weight to mature beef cattle. The weight in pounds is given by , where x is the number of units of the first ingredient and y is the number of units of the second ingredient. How many units of each ingredient will maximize the weight?

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.

If , find and .

Suppose that the joint cost function for two products is dollars. Find the marginal cost with respect to x.

Suppose that x units of one input and y units of a second input result in units of a product. What is the maximum production?

Suppose that the joint cost function for two products is dollars. Find the marginal cost with respect to x.

Evaluate the function at the given values of the independent variables. ; ,