Answered: A large corporation with monopolistic…

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

ChapterP: Prerequisites

Section: Chapter Questions

Problem 17T: A T-shirt company can produce and sell x T-shirts per day. The total cost C (in dollars) for...

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Question

A large corporation with monopolistic control in the marketplace has its average daily costs, in dollars, given by

C =

500

+ 200x + x².

The daily demand for x units of its product is given by

p = 450,000 − 100x dollars.

Find the quantity that gives maximum profit.
x =   units

Find the maximum profit.
$

What selling price should the corporation set for its product?
$

Expert Solution

Step 1

$G i v e n, A v e r a g e D a i l y \cos t, C = 500 / x + 200 x + x^{2} D a i l y d e m a n d, p = 450, 000 - 100 x d o l l a r s N o w, R e v e n u e o f x p r o d u c t = p * x = 450, 000 x - 100 x^{2} T o t a l \cos t = c * x = 500 + 200 x^{2} + x^{3}$

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