Answered

Discover a wealth of knowledge at Westonci.ca, where experts provide answers to your most pressing questions. Explore our Q&A platform to find in-depth answers from a wide range of experts in different fields. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

For a certain company, the cost function for producing x items is C(x)=50x+100 and the revenue function for selling x items is R(x)=−0.5(x−100)2+5,000 . The maximum capacity of the company is 120 items.



The profit function P(x) is the revenue function R(x) (how much it takes in) minus the cost function C(x) (how much it spends). In economic models, one typically assumes that a company wants to maximize its profit, or at least make a profit!



Answers to some of the questions are given below so that you can check your work.



Assuming that the company sells all that it produces, what is the profit function?
P(x)=

Sagot :

abiolataiwo2015

Assuming that the company sells all that it produces, The profit function is: P(x)=-x^/2+50x -100 or P(x)=-0.5x²+50x -100.

Profit function

Profit = R-C = -(x-100)^2/2 +5000 - 50x -100 =

-(x^2 -200x +10000)/2 -50x +4900 =

-x^2/2 +100x -5000 +5000 -50x +4900

Collect like terms

-x^/2+50x -100

Hence,

Profit function = P(x)=-0.5x²+50x -100

Maximum profit generating output  can be determine by taking the derivative and setting it equal to zero

R-C = -x^2/2 + 50x -100

R'-C' = -x + 50 =0

P(0)x = 50

Maximum profit  can be determine by substituting x=50 into the original profit equation, R-C

P(50) =-(1/2)(50)^2 +50(50) -100

P(50)= -1250 + 2500 -100

P(50) = $1150 profit

P(120) =-(1/2)(120)^2 +50(120) -100

P(120)= -3600 + 6000 -100

P(120) = $2300 profit

Therefore the profit function is: P(x)=-x^/2+50x -100 or P(x)=-0.5x²+50x -100.

Learn more about profit function here:https://brainly.com/question/4618859

#SPJ1

Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.