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## For a certain company, the cost function for producing x items is C(x)=50x+200 and the revenue function for selling x items is R(x)=−0.5(x−90)2+4,050. The maximum capacity of the company is 110 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)=       What is the domain of P(x)

For a certain company, the cost function for producing x items is C(x)=50x+200 and the revenue function for selling x items is R(x)=−0.5(x−90)2+4,050. The maximum capacity of the company is 110 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.

1. Assuming that the company sells all that it produces, what is the profit function?

P(x)=

2. What is the domain of P(x)?

Hint: Does calculating P(x) make sense when x=−10 or x=1,000?

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