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.
I want to learn this topic l dont know anything about it
Solve the linear system of equations attached using Gaussian elimination (not Gauss-Jordan) and back subsitution.
Remember that:
A matrix is in row echelon form if
Any row that consists only of zeros is at the bottom of the matrix.
The first non-zero entry in each other row is 1. This entry is called aleading 1.
The leading 1 of each row, after the first row, lies to the right of the leading 1 of the previous row.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.