$($a$)$ For one of its popular computer models, Agility Manufacturing is trying to optimize the

lot sizes for its assembly orders given the requirements in Table $3.$ The following

information has been put together by its Inventory Management Department: Setup cost:

$$\frac{300}{?}$ order; Inventory carrying cost: $$\frac{1}{?}$ unit$/$week; Inventory on hand: $0$ units.

Table $3$

Determine the optimum lot sizing for the company using the Wagner$-$Whitin algorithm.

Assume that the period ending inventory incurs the inventory carrying cost. Specify the

lot sizes over the six weeks and the total cost of the solution with full working explanation.

$(15$ marks$)$