An $8 item will sell 100 units per week . For every $.50 reduction in price , it is predicted that an additional 20 units will be sold . What price will yield maximum revenue for this item?

Answer 1

Let we have x reduction in price. Then new price is (8 - 0.5x) and sale is (100 + 20x).

So, revenue R(x) = (8 - 0.5x)(100 + 20x) = 800 + 110x - 10x²; R'(x) = 110 - 20x = 0; x = 5.5

But we can't reduce price 5.5 timec we have take x = 5 or 6.

Let calculate revenu: R(5) = (8 - 2.5)(100 + 100) = 1100

R(6) = (8 - 3)(100 + 120) = 1100.

Price: 8 - 2.5 = $5.5 and price 8 - 3 = $5 give the same max revenue $1100