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For a certain company, the cost function for producing x items is C (x) = 30x + 150 and the revenue function for selling x items is R (x) = -0.5(x -...
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For a certain company, the cost function for producing x items is

C (x) = 30x + 150 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 140 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!


1: What is the domain and range of C (x)?
2: What is the meaning of the slope and intercept of C (x)?
3: At what production level x will the company receive the most revenue? The maximum revenue occurs when x= ?
4: Assuming that the company sells all that it produces, what is the profit function?
5: The company can choose to produce either 70 or 80 items. What is their profit for each case?

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