Profit-loss analysis. Use the revenue and cost functions from Problem 60 in this exercis...

Profit-loss analysis. Use the revenue and cost functions from Problem 60 in this exercise:

where x is thousands of computers, and R(x) and C(x) are in thousands of dollars. Both functions have domain 1 ≤ x ≤ 25.

(A) Form a profit function P, and graph it, C, and P in the same rectangular coordinate system.

(B) Discuss the relationship between the intersection points of the graphs of I? and C and the x intercepts of P.

(C) Find the x intercepts of P to the nearest hundred computers. Find. the break-even points.

(D) Refer to the graph drawn in part (A). Does the maximum profit appear to occur at the same output level as the maximum revenue? Are the maximum profit and the maximum revenue equal? Explain.

(E) Verify your conclusion in part (D) by finding the output that produces the maximum profit. Find the maximum profit and compare with Problem 58B.

Reference: Problem 60:

Break-even analysis. Use the revenue function from Problem 58, in this exercise and the given cost function: R(x) = x(2,000 - 60x) Revenue function C(x) = 4,000 + 500x Cost function

where x is thousands of computers, and C(x) and R(x) are in thousands of dollars. Both functions have domain 1 ≤ x ≤ 25.

(A) Sketch a graph of both functions in the same rectangular coordinate system.

(B) Find the break-even points.

(C) For what outputs will a loss occur? Will a profit occur?

Reference: Problem 58:

Revenue. The marketing research department for a company that manufactures and sells "notebook" computers established the following price-demand and revenue functions:

where p(x) is the wholesale price in dollars at which x thousand computers can be sold, and R(x) is in thousands of dollars. Both functions have domain 1 ≤ x ≤ 25.

(A) Sketch a graph of the revenue function in a rectangular coordinate system.

(B) find the output (to the nearest hundred computers) that Will produce the maximum revenue. What is the maximum revenue to the nearest thousand dollars?

(C) What is the wholesale price per computer (to the nearest dollar) that produces the maximum revenue?