$($Inventory Management $$ Part $2)$ An item has a unit purchase cost of $$50,$ and an inventory$-$carrying rate

per period of $0\mathrm{.}02.$ The additional data for this product is given below:

Period $12345$

Demand $($units$)750654090$

Fixed Cost $($$$/$order$)100110100105100$

Assuming no backordering is allowed, answer the followings:

$($a$)$ Check whether the demand is lumpy or not.

$($b$)$ Apply the following heuristics on the problem given above.

$($i$)$ Period Order Quantity

$($ii$)$ Silver$-$Meal

$($iii$)$ Part$-$Period Balancing

$($c$)$ Which of the solutions obtained in part $($b$)$ do you select?

$($d$)$ Draw a network diagram to illustrate the given lot sizing problem, and calculate the cost values for each

arc on the network.

$($e$)$ Apply the Wagner$-$Whitin algorithm to determine the optimal order quantities, the optimal inventory

levels, and the minimum sum of the ordering and inventory carrying costs.