Solve the following problem with Excel Solver: $($Leave no cells blank $-$ be certain to enter $"0"$ wherever required. Round your answers to $2$ decimal places.$)$

$$

Minimize Z$=6$A $+8$B$\mathrm{.}4$A $+12$B$1024$A $+15$B$371$B$11$

$$

PRODUCT

MACHINE TYPEX$1$X$2$X$3$Milling machine$823$Lathe$430$Grinder$201$

$$

The available time in machine hours per week is

$$

$$MACHINE HOURS PER WEEKMilling machines$800$Lathes$480$Grinders$320$

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

Unit profits for the three products are

$$

$$UNIT PROFITSX$1$$$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.$)$

s$.$t

b$.$Solve these equations using the Excel Solver.$($Round your answers to the nearest whole number.$)$

c$.$How much of each constraint or resource is unused?$($Leave no cells blank $-$ be certain to enter $"0"$ wherever required. Round your answers to the nearest whole number.$)$

d$-1.$Would the machines work at capacity?

d$-2.$WillX$3$be at maximum sales capacity?

multiple choice

Yes

No

e$.$Suppose that an additional $200$ hours per week can be obtained from the milling machines by working overtime. The incremental cost would be $$1\mathrm{.}50$ per hour. What would be the allowable increase $($from the excel sensitivity report$)$ in overtime when compared to additional hours that can be obtained?