Q16. - Algebra 2

Question

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 soccer balls and 2 hours to make 60 volleyballs. Cutting has 500 hours available, and sewing has 450 hours available.

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

Step-by-Step Solution

Answer

The maximum profit is $56250. 

Step 1 – Write the profit maximize function

It is given that a sporting goods manufacturer makes a $5 profit on soccer balls and a $4 profit on volleyballs.

Therefore, the maximize profit function is,

$f=5x+4y$

Step 2 – Rewrite the corner points of the feasible region from Ex-15

The corner points of the shaded region are $O(0,0),A(11250,0),B(5250,7200)$ and $C(0,10000).$

Step 3 – Evaluating the maximum and minimum value

The maximization function is $f=5x+4y.$

At point $O(0,0),$

  $f=0$

At point $A(11250,0),$

$f=56250$

At point $B(5250,7200),$

$f=55050$

At point $C(0,10000),$

$f=40000$

Thus, the maximum profit is $56250.