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?

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AlonsoDehner AlonsoDehner · Answer 1 · 2019-12-26T17:37:13+01:00

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[tex]= 300*350 = 105000[/tex]

After rebate of x times 30 dollars we have

New revenue

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

Equate first derivative to 0 to get

x=[tex]\frac{12000}{3600} =3.333[/tex]

i.e. 3 times rebate will maximize its revenue