a) appears to contain some typos
I will do it my way
let the number of $14 rebates be
Return = number sold x price of each unit
= (450 - 14n)(1400 + 140n)
dR/dn = (450-14n)(140) + (1400+140n)(-14)
= 63000 - 1960n - 19600 - 1960n
= 0 for a max of Revenue
3920n = 43400
n = 11.07
I will assume there is no partial rebate, so the greatest revenue is obtained with 11 rebates
c) looks like another typo, no cost function is shown
simply subtract the cost function from the revenue function obtained above and proceed like I did
A manufacture has been selling 1400 television sets a week at $450 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 , where is the number of the television sets sold per week and 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 , how should it set the size of the rebate to maximize its profit?
1 answer
1 answer