SOLUTION: A clothing store sells 140 jackets in a season for $15 each. The manager determined that for each $1 decrease in price, it would result in 20 more jackets being sold. a) Write

Question 1181596: A clothing store sells 140 jackets in a season for $15 each. The manager determined that for each $1 decrease in price, it would result in 20 more jackets being sold.
a) Write a quadratic function in standard form that models this situation.
b) What price should the manager charge to maximize revenue?
c) What is the maximum revenue?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
price * quantity = revenue.
when price = 15 and quantity = 140, revenue = 15 * 140 = 2100.
let x = the decrease in price.
let 20x equal the number of jackets.
price * quantity = revenue formula becomes:
(15 - x) * (140 + x) = revenue.
when x = 0, this becomes 15 * 140 = 2100, same as before.
when x = 1, the formula becomes 14 * 160 = 2240
when x = 2, the formula becomes 13 * 180 = 2340.
this equation can be graphed as shown below.

as can be seen, this is a quadratic equation.
it will rise to a maximum revenue at x = 4 and then decline after that.
the display is in (x,y) format.
when x = 4, y = 2420
the price becomes 15 - 4 = 11 and the revenue becomes 140 + 20 * 4 = 220 and the revenue becomes 11 * 220 = 2420.

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