SOLUTION: A sporting goods manufacturer makes a 5$ profit on soccer balls and $4 profit on volleyballs. Cutting requires 2 hours to make 75 soccer balls and 3 hours to make 60 volleyballs. S

Question 185217This question is from textbook Algebra 2
: A sporting goods manufacturer makes a 5$ profit on soccer balls and $4 profit on volleyballs. Cutting requires 2 hours to make 75 soccer balls and 3 hours to make 60 volleyballs. Sewing needs 3 hours to make 75 soccer balls and 2 hours to make 60 volleyballs. Cutting has 500 hours available, and Sewing has 450 hours available.
1. How many soccer balls and volleyballs should be made to maximize the profit?
2. What is the maximum profit the company can make from these two products?This question is from textbook Algebra 2

Answer by josmiceli(6784) (Show Source):
You can put this solution on YOUR website!
Let = number of soccer balls to be made
Let = number of volleyballs to be made
Let = profit from both
given:
(1)
(2)
(3)
------------------------------------
Multiply both sides of (2) and (3) by
(2)
(3)
------------------------------
I'll plot (x-axis) and (y-axis) (1),(2),and (3)

The axes are scaled to thousands
To find the intersection I'll multiply (1) by
and (2) by Then subtract (3) from (2)
(2)
(3)
(4)
(4)
Putting this back in (2)
Multiply both sides of (2) and (3) by
(2)
(4)
(4)
(4)
7200 volleyballs and 5250 soccer balls are made to maximize profits
The maximum profit is:
(1)
(1)
(1)
(1)
The maximum profit is $55,050

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