The total costs for a company are given by C(x) = 3500 + 60x + x2 and the total revenues are given by R(x) = 180x.
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A company keeps records of the total revenue (money taken in) in thousands of dollars from the sale of x units (in thousands) of a product. It determines that total revenue is a function R(x) given by R(x) = 300x - x^2. It also keeps records of the total cost of producing x units of the same product. It determines that the total cost is a function C(x) given by C(x) = 40x + 1600. a) Find the break-even points for this company. (Round answer to nearest 1000.) b) Determine at what point profit is at a maximum. What is the maximum profit? How many units must be sold in order to achieve maximum profit?
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