1)

A calculator manufacturer has the total cost function C(x) = 32x + 6458 and the total revenue function R(x) = 67x.

(a) What is the equation of the profit function P(x) for the calculator? P(x) =

(b) What is the profit on 2000 units? P(2000) = $

2)Suppose a radio manufacturer has the total cost function

C(x) = 26x + 3250

and the total revenue function

R(x) = 91x.

(a) What is the equation of the profit function for this commodity? P(x) =

(b) What is the profit on 30 units?

P(30) =

Interpret your result.

The total costs are less than the revenue.The total costs are more than the revenue. The total costs are exactly the same as the revenue.

(c) How many radios must be sold to avoid losing money? radios

3)Suppose a computer manufacturer has the total cost function C(x) = 84x + 3168 and the total revenue function R(x) = 372x.

(a) What is the equation of the profit function P(x) for this commodity? P(x) =

(b) What is the profit on 340 items? P(340) = $ (c) How many items must be sold to avoid losing money? x = items

4)

A linear cost function is

C(x) = 6x + 510. (Assume C is measured in dollars.)

(a) What are the slope and the C-interpret?

slope		m	=
C-intercept		C	=

(b) What is the marginal cost? MC = What does the marginal cost mean?

Each additional unit produced reduces the cost by this much (in dollars).Each additional unit produced costs this much (in dollars). If production is increased by this many units the cost increases by $1.If production is increased by this many units the cost decreases by $1.

(c) How are your answers to parts (a) and (b) related?

C-intercept

Slope

= marginal cost.Slope = fixed costs, and C-intercept = marginal cost.

Slope

C-intercept

= marginal cost.Slope = marginal cost, and C-intercept = fixed costs. (d) What is the cost of producing one more item if 50 are currently being produced? $ What is the cost of producing one more item if 100 are currently being produced? $

5)

Let

C(x) = 6x + 550 and R(x) = 28x.

(a) Write the profit function P(x). P(x) =

(b) What is the slope of the profit function?

m =

(c) What is the marginal profit? MP = (d) Interpret the marginal profit.

Each additional unit sold increases the profit by this much.Each additional unit sold decreases the profit by this much. This is the smallest number of units that can be sold in order to make a profit.The profit is maximized when this many units are sold.