# maximizing profit

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A manufacture has been selling 1750 television sets a week at \$540 each. A market survey indicates that for each \$14 rebate offered to a buyer, the number of sets sold will increase by 140 per week.

a) Find the function representing the demand p(x), where x is the number of the television sets sold per week and p(x) is the corresponding price.
p(x)=-.1x+715

b) How large rebate should the company offer to a buyer, in order to maximize its revenue?
=182.5

c) If the weekly cost function is 157500 + 180 x, how should it set the size of the rebate to maximize its profit?

the answers to A and B are right but i don't know how to do part c, could someone explain how to find part c?

• maximizing profit - ,

You would solve c) in nearly the same method you used to solve b). Always always always, maximize provits by setting marginal cost (MC) = marginal revenue (MR). MR is the first derivitive of total revenue. Since you got b) right, you probably correctly calculated MR = 715 - .2x. (Then you maximized by setting this equal to zero and solving for x -- correct??)

For c) set MR = MC. MC is the first derivitive of the Total cost function, so MC is simply 180.

Take it from here.

• maximizing profit - ,

how did you get part a