1. ## profit equation

A spoorting goods manufactruer makes a $5 profit on soccer balls and a$4 profit on volleyballs. Cutting requires 2 hours to make 75 soccer balls and 3 hours to make 60 volleyballs. Sweing 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.

How many soccer balls and volleyballs should be made to maximize the profit?

What is the maximum profit the company can make from these two products?

2. Originally Posted by s2011
A spoorting goods manufactruer makes a $5 profit on soccer balls and a$4 profit on volleyballs. Cutting requires 2 hours to make 75 soccer balls and 3 hours to make 60 volleyballs. Sweing 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.

How many soccer balls and volleyballs should be made to maximize the profit?

What is the maximum profit the company can make from these two products?
Let x = the number of soccer balls
Let y = the number of volleyballs

You can't make a negative number of balls, so you're first two constraints would be:

$\displaystyle \boxed{x \ge 0}$ and $\displaystyle \boxed{y \ge 0}$

You're going to be cutting and sewing, so it makes sense to find out how much time it takes to cut and sew one soccer ball and one volleyball.

If it takes 2 hours of cutting to make 75 soccer balls (SB), how many hours of cutting does it take to make 1 soccer ball?

75 SB in 2 hrs means 1 SB in $\displaystyle \frac{2}{75}$ hrs.

Use similar logic to determine how long it takes to cut one volleyball (VB).

60 VB in 3 hrs means 1 VB in $\displaystyle \frac{3}{60}=\frac{1}{20}$ hrs.

The limitation on cutting hours is 500 hours. Now you can set up your third constraint,

$\displaystyle \boxed{\frac{2}{75}x+\frac{1}{20}y \leq 500}$

Now, go work on the sewing part to come up with your 4th and final constraint. Use the same logic as with cutting.