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 ) = − 50 p 2 + 1700 p − 12 , 000 , where p is the price per shirt and f ( p ) is the monthly profit based on that price. ( See Example 4 ) 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.
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 ) = − 50 p 2 + 1700 p − 12 , 000 , where p is the price per shirt and f ( p ) is the monthly profit based on that price. ( See Example 4 ) 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.
Solution Summary: The author explains how to calculate the maximum profit for a company by comparing the equation with the quadratic equation.
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
)
=
−
50
p
2
+
1700
p
−
12
,
000
, where p is the price per shirt and
f
(
p
)
is the monthly profit based on that price. (See Example 4 )
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.
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