The monthly profit for a small company that makes long-sleeve T-shirts depends on the price per shirt. If the price is too high, sales will drop. If the price is too low, the revenue brought in may not cover the cost to produce the shirts. After months of data collection, the sales team determines that the monthly profit is approximated by f(p) = -50p²+1700p-12,000, where p is the price per shirt and f(p) is the monthly profit based on that price. (a) Find the price that generates the maximum profit. (b) Find the maximum profit. (c) Find the price(s) that would enable the company to break even. If there is more than one price, use the "and" button.

The monthly profit for a small company that makes long-sleeve T-shirts depends on the price per shirt. If the price is too high, sales will drop. If the price is too low, the revenue brought in may not cover the cost to produce the shirts. After months of data collection, the sales team determines that the monthly profit is approximated by f(p) = -50p²+1700p-12,000, where p is the price per shirt and f(p) is the monthly profit based on that price. (a) Find the price that generates the maximum profit. (b) Find the maximum profit. (c) Find the price(s) that would enable the company to break even. If there is more than one price, use the "and" button.

Intermediate Algebra

19th Edition

ISBN:9780998625720

Author:Lynn Marecek

Publisher:Lynn Marecek

Chapter9: Quadratic Equations And Functions

Section9.6: Graph Quadratic Functions Using Properties

Problem 281E: In the following exercises, solve. Round answers to the nearest tenth. 281. A computer store owner...

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In the following exercises, solve. Round answers to the nearest tenth. 283. A retailer who sells fashion boots estimates that by selling them for x dollars each, he will be able to sell 70x boots a week. Use the quadratic function R(x)=x2+70x to find the revenue received when the average selling price of a pair of fashion boots is x. Find the selling price that will give him the maximum revenue, and then find the amount of the maximum revenue.
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