Drexel Shoes has received a large order for leather loafers and suede boots. They employ three shoemakers, and

the number of hours needed to make all the leather loafers, the number of hours needed to make all the suede boots,

the number hours each shoemaker has available to work on the order, and the cost per hour are as follows:

Shoemaker $1$ Shoemaker $2$ Shoemaker $3$

Hours Required to Complete All the Leather Loafers $504230$

Hours Required to Complete All the Suede Boots $604835$

Hours Available for the Order $403035$

Cost per Hour $$36$ $$42$ $$55$

For example, if Shoemaker $1$ spent half of his available time on each type of shoe, he would supply $20$ out of

the $50,$ or $40\%,$ of the hours needed for the leather loafers, and $20$ out of $60,$ or $33\mathrm{.}33\%,$ of the hours

needed for the suede boots. Help Drexel Shoes minimize their total cost while meeting the demand.

a$)$ If each of the shoemakers was available for overtime, would Drexel find it useful? If so$,$ how

much would they be willing to pay for the overtime?

b$)$ If Shoemaker $2$ asked for a raise to $$44$ per hour, how would it affect the optimal solution? How would

the total cost change?

c$)$ Shoemaker $1$ receives additional training and can now make all the leather loafers in $46$ hours and all the

suede boots in $56$ hours. How will this affect the total cost?

d$)$ If the order size for the leather loafers increases by $10\%,$ how would this affect the total cost?