Question

A store has been selling 300 DVD burners sold per week at 350 each. A market survey indicates that for each $ 30 rebate offered to buyers, the number of units sold will increase by 60 a week. Find the demand function and the revenue function. How large a rebate should the store offer to maximize its revenue?

Answer 1

Answer:

3 times rebate will maximize its revenue

Step-by-step explanation:

Given that a store has been selling 300 DVD burners sold per week at 350 each

A market survey indicates that for each $ 30 rebate offered to buyers, the number of units sold will increase by 60 a week.

If x times rebate is offered then units sold would be 300+60x

Thus original revenue$= 300*350 = 105000$

After rebate of x times 30 dollars we have

New revenue

$R(x) = (300+60x)(350-30x)\\= 105000+12000x-1800x^2\\R'(x) = 12000-3600x\\\\R"(x) = -3600$

Equate first derivative to 0 to get

x=$\frac{12000}{3600} =3.333$

i.e. 3 times rebate will maximize its revenue