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?
Question content area bottom
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.)
(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.)
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