Question

A popular designer purse sells for $500 and 45,000 purses are sold each month. The marketing specialists have done some research and discovered that for each $20 decrease in price, they can sell 5,000 more purses each month. How much should the company charge for the purse so they can maximize their monthly revenue? (Hint: let x be the number of $20 decreases)

Answer 1

revenue = (500 - 20 x)(45000 + 5000 x)
... = 22500000 +1600000 x - 100000 x^2

xmax = -1600000 / (2 * -100000)