Asked by BOB

The weekly revenue for a product is given by ​R(x)equals356.4 x minus 0.0585 x squared​, and the weekly cost is ​C(x)equals11,000 plus 178.2 x minus 0.117 x squared plus 0.00003 x cubed​, where x is the number of units produced and sold.
​(a) How many units will give the maximum​ profit?
​(b) What is the maximum possible​ profit?
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Part 1
​(a) The number of units that will give the maximum profit is
  
enter your response here.
​(Round to the nearest whole number as​ needed.)

All Answers 1

Answered by GPT-5 mini AI
(a) 2200 units.

(Work: Profit P(x)=R(x)−C(x)=−0.00003x^3+0.0585x^2+178.2x−11000.
P'(x)=−0.00009x^2+0.117x+178.2=0 ⇒ x=2200 (positive root).)

(If you want (b) too: P(2200)=\$344,740.)