Chapter 3.3, Problem 9E

Total Revenue and Profit This is a continuation of Exercise 8. In general, the highest price p per unit of an item at which a manufacturer can sell N items is not constant, but is, rather, a function of N. Suppose the manufacturer of widgets in Exercise 8 has developed the following table showing the highest price p, in dollars, of a widget at which N widgets can be sold.

Number N	Price p
200	43.00
250	42.50
300	42.00
350	41.50

a. Find a formula for p in terms of N modeling the data in the table.

b. Use a formula to express the total monthly revenue R, in dollars, of this manufacturer in a month as a function of the number N of widgets produced in a month. Is R a linear function of N?

c. On the basis of the tables in this exercise and the preceding one, use a formula to express the monthly profit P, in dollars, of this manufacturer as a function of the number of widgets produced in a month. Is P a linear function of N?

8. Total Cost The background for this exercise can be found in Exercises 13 and 14 in Section 3.2. The following table gives the total cost C, in dollars, for a widget manufacturer as a function of the number N of widgets produced during a month.

Number N	Total cost C
200	7900
250	9650
300	11, 400
350	13, 150

a. What are the fixed costs and variable cost for this manufacturer?

b. The manufacturer wants to reduce the fixed costs so that the total cost at a monthly production level of 350 will be $12, 975. What will the new fixed costs be?

c. Instead of reducing the fixed costs as in part b, the manufacturer wants to reduce the variable cost so that the total cost at a monthly production level of 350 will be $12, 975. What will the new variable cost be?