A sporting goods manufacturer 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. Sewing needs 3 hours to make 75 soccerballs and 2 hours to make 60 volleyballs. Cutting has 500 hours avaliable, and sewing has 450 hours availible. What is the maximum profit the company can make from these two products?

List constraints and variables

your variables is number of each types of balls, the constraints are sewing and cutting hrs.

can u please name the constraits

sewing hrs, cutting hrs.

Constraints:

1. Cutting requires 2 hours to make 75 soccer balls.
2. Cutting requires 3 hours to make 60 volleyballs.
3. Sewing needs 3 hours to make 75 soccer balls.
4. Sewing needs 2 hours to make 60 volleyballs.
5. Cutting has 500 hours available.
6. Sewing has 450 hours available.

Variables:
Let's define the variables:
x = the number of soccer balls produced using cutting process.
y = the number of volleyballs produced using cutting process.
z = the number of soccer balls produced using sewing process.
w = the number of volleyballs produced using sewing process.

Profit:
The profit on each soccer ball is $5.
The profit on each volleyball is $4.

We need to maximize the profit, which can be calculated as:
Profit = (5 * x) + (4 * y) + (5 * z) + (4 * w)

Now, we can write the objective function and constraints based on the given information.