A store has been selling 400 Blu-ray disc players a 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

2.5 times rebate will maximize its revenue

Explanation:

From the question, the store has been selling 400 Blu-ray disc players a week at $350 each.

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

Let say that the rebate is offered at "x" times, then units sold would be 400+60x

We can calculate the original revenue as (400*350)= $140000

After rebate of x times 30 dollars New revenue can be calculated as

R(x)=(400+60x)(350-30x)

= -1800x^2 +900x+140000

R'(x)=9000-3600x

R"(x)=-3600

If first derivatives is equted to zero

0=9000-3600x

X= 9000/3600

X=2.5

Which means 2.5 times rebate will maximize its revenue

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