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
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-> 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
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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?
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.
