A manufacturer has been selling 1000 flat-screen TVs a week at $400 each. A mark

Question

A manufacturer has been selling 1000 flat-screen TVs a week at $400 each. A market survey indicates that for each $10 rebate offered to the buyer, the number of TVs sold will increase by 100 per week. (a) Find the demand function (price p as a function of units sold x). (b) How large a rebate should the company offer the buyer in order to maximize its revenue?  (c) If its weekly cost function is C(x) = 60,000 + 130x, how should the manufacturer set the size of the rebate in order to maximize its profit?

Explanation / Answer

slope of demand function = change in sales/change in rebate
= 80/10
= 8

When rebate = 0, demand = 1000.
? d(r) = 8r + 1000
-----------------
Revenue = demand * (price - rebate)
= (8r + 1000)(400 - r)
= (8r + 1000)(-r + 400)
= -8r

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