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Section $2$

$(Q,R)$ : Suppose the weekly demand for an item is approximately normal with the distribution of $DN(68,{16}^2)$ units over a $50-$week operating year. The company pays $$4\mathrm{.}2$ for each unit and sells each for $$12\mathrm{.}5.$ In addition, they estimate that the annual holding cost is $25$ percent of the unit's cost. Finally, the supplier contract states there is a cost of $$71\mathrm{.}4$ to place an order $($largely managerial and clerical costs$).$ Assume a nine$-$week lead time.

What is the distribution of the demand during lead time?

a$.N(612,2304)$

b$.N(612,48)$

c$.N(675,15)$

d$.N(675,225)$