Exam 4: Lines parabolas and Systems

Two species of monkey,A and B,live in one enclosure at the zoo where they are fed two vitamin supplements.Each day they receive 350 grams of the first supplement and 500 grams of the second supplement.Each monkey of species A requires 25 g of the first supplement and 10 g of the second supplement.Each monkey of species B requires 15 g of the first supplement and 30 g of the second supplement.How many of each species of monkey will the enclosure support so that all of the supplements are consumed each day?

How much of each of a 25% (by volume)chemical solution and a 32% solution must be combined to make 75 cubic centimeters of a 28% solution?

The demand function for a manufacturer's product is p = f(q)= 800 - 2q,where p is the price (in dollars)per unit when q units are demanded (per week).Find the level of production that maximizes the manufacturer's total revenue.

The demand function for an appliance company's line of washing machines is where p is the price (in dollars)per unit when q units are demanded (per week)by consumers.Find the level of production that will maximize the manufacturer's total revenue,and determine this revenue.

Find the range of the function y = f(x)= 4 - 16x + 1.

Find the Break Even Point for a product whose Total Revenue, ,(in $)and Total Cost, ,(in $)are as follows: = (10q - 25)q = 2000 + 75q

Suppose that a manufacturer will place on the market 80 units of a product when the price is $10 per unit,and 100 units when the price is $12 per unit.Find the supply equation for the product assuming that price p and quantity q are linearly related.

Consider the restricted quadratic function f (x)= + 4x + 6 on x ≥ -2.Determine the restricted function (x)graphically.Graph both f(x)and (x)on the same xy-plane.

Solve the following system algebraically:

Solve the following system algebraically:

Find the x-coordinate of the vertex of a graph of the quadratic function

Solve the system

Suppose f is a linear function such that f(0)= 6 and f(3)= 4.Find f(x).

Suppose that consumers will demand 800 units of a product when the price is $10 per unit,and 1000 units when the price is $8 per unit.Find the demand equation for the product assuming that price p and quantity q are linearly related.

Solve the following system algebraically:

In testing an experimental diet for goats,it was determined that the (average)live weight w (in kilograms)of a goat was statistically a linear function of the number of days d after the diet was started where 0 ≤ d ≤ 100.The weight of a goat starting the diet was 12 kg and 25 days later it was 20 kg.Determine w as a linear function of d and find the average weight of a goat when d = 80.

Solve the system:

Suppose that the supply and demand equations for a certain product are and respectively,where p represents the price per unit in dollars and q represents the number of units per time period. (a)Find the equilibrium price algebraically. (b)Find the equilibrium price when a tax of 50 cents per unit is imposed.

State whether f(x)= 12 - 24x + 10 has maximum or minimum value and find that value.

Two species of fish,A and B,are raised in one pond at a fish farm where they are fed two vitamin supplements.Each day they receive 100 grams of the first supplement and 200 grams of the second supplement.Each fish of species A requires 20 mg of the first supplement and 30 mg of the second supplement.Each fish of species B requires 10 mg of the first supplement and 40 mg of the second supplement.How many of each species of fish will the pond support so that all of the supplements are consumed each day? Use elimination by substitution to solve the systems.