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?

Question

Haleigh Estes

Business

13 April, 08:58

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?

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Answers (1)

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Brynlee David · Answer 1

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