If y is the number of rebates, then the revenue is
r(y) = (420-16y)(1300+160y)
assuming only enough sets are made to sell out, then x = 1300+160y
so, the profit is revenue less cost
p(y) = r(y) - c(1300+160y)
= (420-16y)(1300+160y) - (91000+140(1300+160y))
= -2560y^2 + 24000y + 273000
This has a maximum at y=75/16
so, a rebate of $75 will maximize the profit
as always, check my math and reasoning.
A manufacture has been selling 1300 television sets a week at $420 each. A market survey indicates that for each $16 rebate offered to a buyer, the number of sets sold will increase by 160 per week.
If the weekly cost function is 91000+140x, what value of the rebate maximizes the profit? dollars
1 answer