A manufacturer has been selling 1000 television sets a week at $500 each. A mark

Question

A manufacturer has been selling 1000 television sets a week at $500 each. A market survey indicates that for each $10 rebate offered to the buyer, the number of sets sold will increase by 100 per week. Round your answers to the nearest dollar.

(a) Find the linear demand function (price as a function of units sold).

(b) How large a rebate should the company offer the buyer in order to maximize its revenue?

(c) If the company experiences a cost of C(x) = 76,000 + 110x, how should the manufacturer set the size of the rebate in order to maximize its profit?

Explanation / Answer

Let p(x) be the demand function with x as the number of TV sets demanded. As given

in the problem, p(x) going down by $10 would cause x to increase by 100. Therefore

the slope of the graph for the demand function is ?10/100= ?1/10

. We also know that p(1000) = 450. Hence we have

?1/10=p(x)

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