$($EOQ with Zero$-$Demand Sub$-$Cycles$)$ Consider the following modification to the EOQ problem. Suppose that, each time an order is placed, the demand is

initially $0$ for a fraction $\backslash$beta of the cycle, and then the demand occurs at a rate of $\backslash$lambda $/(1\backslash$beta $)$

for the duration of the cycle. One can show $($you need not$)$ that the total cycle length

is still Q$/\backslash$lambda $,$ just like in the original EOQ model, and the cycle is divided as shown in

Figure $3\mathrm{.}21.$ Calculate the optimal order quantity, Q$$

$.$