Question

Asportinggoodsmanufacturermakesa\(5profitonsoccerballsanda\)4profitonvolleyballs.Cuttingrequires2hourstomake75soccerballsand3hourstomake60volleyballs.Sewingneeds3hourstomake75soccerballsand2hourstomake60volleyballs.Cuttinghas500hoursavailable,andsewinghas450hoursavailable.

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

Short answer

The maximum profit is $56250.

Step-by-step solution

– Write the profit maximize function

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

Therefore, the maximize profit function is,

$f=5x+4y$

– 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$C(0,10000).$

– 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.