A manufacturer has been selling 1000 television sets a week at $400 each. A mark

Question

A manufacturer has been selling 1000 television sets a week at $400 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). I got 400-10x, which is wrong.

b) How large a rebate should the company offer the buyer in order to maximize its revenue? I got 150, but not sure how.

c) If the company experiences a cost of C(x) = 64,000 + 110x, how should the manufacturer set the size of the rebate in order to maximize its profit?

Explanation / Answer

Let x = the number of rebates
Then the price of a set is: 500-10x and the number of sets sold is: 1000+100x
So the total revenue is:
R(x) = (500-10x)(1000+100x)
Expanded, that's:
R(x) = -1000x

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