$3\mathrm{.}2$ The setup cost for the assembly of a product is $$1500$ per order, and the inventory

carrying cost is $$4\mathrm{.}00$ per product per week. The estimated net requirements for the

product for the next eight weeks are as follows:

For part $($b$)$ assume the average annual demand is $65,000.$

$5\mathrm{.}2$ Consider exercise $3\mathrm{.}2.$ If backorders are allowed, the cost would be $$2\mathrm{.}50$ per unit per

period.

$($a$)$ Solve the problem where backorders are not allowed using the optimization

method.

$($b$)$ Suppose backorders are allowed except for the last period. Use the optimization

method and compare the solutions with part $($a$)$ and also with the solution of

exercise $3\mathrm{.}2.$

$($c$)$ Suppose backorders are allowed except for the last period and capacity is $350.$

Solve the problem and compare to the solution of exercise $4\mathrm{.}2.$

$5\mathrm{.}9$ Consider exercise $5\mathrm{.}2.$ Backorder would cost $$2\mathrm{.}5$ per unit per period. Suppose the

weights of importance for the normalized objectives of total cost, total inventory,

and total number of backlog are $0\mathrm{.}6,0\mathrm{.}1,$ and $0\mathrm{.}3,$ respectively. Use the MOO lot$-$

sizing approach to determine the optimal solution. For this solution, report total

cost$,$ lot size for each period, inventory level for each period, and backlog for each

period.