A component used in a manufacturing facility is ordered from an outside supplier. The

time$-$phased net requirements for the component over the next $7$ weeks are $5,25,17,15,$

$25,13,$ and $27.$ Assume a holding cost of $$1\mathrm{.}5$ per week and a setup cost of $$42.$

$1)$ Determine the order policy for this item over the next $7$ weeks based on Silver$-$Meal

heuristic.

$2)$ Assume there is a capacity constraint to the lot sizing

a$.$ Suppose that the maximum order size is $15$ per week. Does there exist a feasible

solution?

b$.$ Suppose that the maximum order size is $25$ per week. Use lot$-$shifting technique to

obtain a feasible solution $($without using holding and setup cost$).$

c$.$ Suppose that the maximum order size is $25$ per week. Improve the solution

obtained in Part $($b$)$