posted by Miranda on .
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.
b) How large rebate should the company offer to a buyer, in order to maximize its revenue?
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?
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.
how did you get part a