Use probabilistic inventory control$-$continuous :Slaq Computer Company manufactures notebook computers. The economic lifetime of a

particular model is only $4$ to $6$ months, which means that Slaq has very little time to make

adjustments in production capacity and supplier contracts over the production run. For a

soon$-$to$-$be$-$introduced notebook, Slaq must negotiate a contract with a supplier of

motherboards. Because supplier capacity is tight, this contract will specify the number of

motherboards in advance of the start of the production run. At the time of contract

negotiation, Slaq has forecasted that demand for the new notebook is normally distributed

with a mean of $10,000$ units and a standard deviation of $2,500$ units. The net profit from a

notebook sale is $$500($note that this includes the cost of the motherboard, as well as all other

material, production, and shipping costs$).$ Motherboards cost $$200$ and have no salvage

value $($i$.$e$.,$ if they are not used for this particular model of notebook, they will have to be

written off $).$

$($a$)$ Use the news vendor model to compute a purchase quantity of motherboards that

balances the cost of lost sales and the cost of excess material.

$($b$)$ Comment on the appropriateness of the news vendor model for this capacity planning

situation. What factors are not considered that might be important?