Thread: Maximizing profit

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?
I remember that part c is the cost equation minus the revenue equation but i don't know which one is the revenue equation and when i tried with what i thought it was i got it wrong

Originally Posted by mrderson

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

...i don't know how to do part c

You have found the "revenue" function and are given the "cost" function. Now use the fact that "profit" is the difference between the revenues (income) and costs (outgo), and create a "profit" function.

Differentiate and maximize.