Problem A$-3($Static$)$

A manufacturing firm has discontinued production of a certain unprofitable product line. Considerable excess production capacity was created as a result. Management is considering devoting this excess capacity to one or more of three products: X$1,$ X$2,$ and X$3.$

Machine hours required per unit are

PRODUCT

MACHINE TYPE X$1$ X$2$ X$3$

Milling machine $823$

Lathe $430$

Grinder $201$

The available time in machine hours per week is

MACHINE HOURS PER WEEK

Milling machines $800$

Lathes $480$

Grinders $320$

The salespeople estimate they can sell all the units of X$1$ and X$2$ that can be made. But the sales potential of X$3$ is $80$ units per week maximum.

Unit profits for the three products are

UNIT PROFITS

X$1$ $ $20$

X$26$

X$38$

a$.$ Set up the equations that can be solved to maximize the profit per week. $($Leave no cells blank $-$ be certain to enter $"0"$ wherever required.$)$