Answer to Question #302474 in Financial Math for Lia

Question

The marketing research department for a company that manufactures and sells laptop computers

established the following price-demand and cost functions, respectively:

p (x) = 1,000 - 25x

C(x) = 2,150 + 250x

where p() is the wholesale price in United States dollars at which y thousand laptops can be sold and

C(x) is in thousands of dollars. The domain of both functions is, 1 < x < 10.

Formulate a revenue function (R (x), and a profit function P(x), assuming both are in

thousands of dollars.

Graph the functions C(x), R(x) and P(x) using the same cartesian plane.

Find the value of r that will produce the maximum revenue. What is the maximum revenue to

the nearest thousand dollars?

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

revenue?

Find, algebraically, the break-even points.

For what values of y will a loss and a profit occur?

Find the value of y that produces the maximum profit. Find the maximum profit.