A manufacture has been selling 1700 television sets a week at 420dollars each. A

Question

A manufacture has been selling 1700 television sets a week at 420dollars each. A market survey indicates that for each 21 -dollarrebate offered to a buyer, the number of sets sold will increase by210 per week.
a) Find the demand function p(x), where x is the number of the television sets soldper week, assuming that p(x) is linear.
p(x)=

b) How large of a rebate should the company offer to a buyer, inorder to maximize its revenue?
c) If the weekly cost function is 119000 + 140 x, how should it set the size ofthe rebate to maximize its profit?

Explanation / Answer

p(x)==420x assume amount of rebate is 21y revenue is (420-21y)(1700+210y), on solving, y=5.95 rebate offered should be 125 c profit=(420+21y)(1700+210y)-(119000+140(1700+210y)) solve, y=2.62 rebate =55

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