Question

A store has been selling 100 DVD burners a week at $450 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:

a rebate of 200 dollars will generate 500 sales

with a revenue of 125,000

Explanation:

We need to maximize the total revenue which is:

TR = Price x Quantity. First we define each of these:

P = (450 - 30X)

Q = (100 + 60X)

Being X the cash rebate

We now replace this into the TR formula:

TR = P x Q = (450 -30X) (100 + 60X)

TR = -1800x2 +27,000x -3,000x + 45,000

TR = -1800x2 +24,000x + 45,000

as this is a quadratic function: a: -1,800 b = 24,000 c = 45,000

the maximum revenue will be at the vertex: -b/2a

-24,000/2(-1,800) = 6.67

now we multiply by 30: 6.67 x30 = 200 dollars

which bring 60 x 6.67 = 400 new customers

250 x (100 +400) = 250 x 500 = 125,000