Chapter 2.5, Problem 85E

5 Use a spreadsheet to numerically verify the result of Exercises 1-55.

For Exercises 23-28 find the maximum profit and the number of units that must be produced and sold in order to yield the maximum profit, Assume that revenue, $\text{R}\left(\text{x}\right),and\cos t,\text{C}\left(\text{x}\right),areindollarsfor$

Exercises 23-26

Maximizing profit. Raggs, Ltd., a clothing firm, determines that in order to sell x suits, the price per suit must be

$P=150-0.5x.$

It also determines that the total cost of producing x suits is given by

$C\left(x\right)=4000+0.25x^2.$

a. Find the total revenue, $R\left(x\right)$

b. Find the total profit, $P\left(x\right)$

c. How many suits must the company produce and sell in order to maximize profit?

d. What is the maximum profit?

e. What price per suit must be charged in order to maximize profit?