In all problems involving days, a 365-day year is assumed. Profit–loss analysis....

In all problems involving days, a 365-day year is assumed.

Profit–loss analysis. Use the cost and revenue functions from Problem 88.

(A) Write a profit function and graph it in a graphing calculator.

(B) Determine graphically when P = 0, P < 0, and P > 0 to the nearest unit.

(C) Determine graphically the maximum profit (to the nearest thousand dollars) and the output (to the nearest unit) that produces the maximum profit. What is the wholesale price of the radio (to the nearest dollar) at this output? [Compare with Problem 88C.]

Reference:

Break-even analysis. The research department in a company that manufactures AM/FM clock radios established the following price-demand, cost, and revenue functions:

where x is in thousands of units, and C(x) and R(x) are in thousands of dollars. All three functions have domain 1 ≤ x ≤ 40.

(A) Graph the cost function and the revenue function simultaneously in the same coordinate system. *

(B) Determine algebraically when R = C. Then, with the aid of part (A), determine when R < C and R > C to the nearest unit.

(C) Determine algebraically the maximum revenue (to the nearest thousand dollars) and the output (to the nearest unit) that produces the maximum revenue. What is the wholesale price of the radio (to the nearest dollar) at this output?