T $18\mathrm{.}3-9.$ Reconsider Prob. $18\mathrm{.}3-3.$ Because of the popularity of the Power model computer, Tim Madsen has found that customers are willing to purchase a computer even when none are currently in stock as long as they can be assured that their order will be filled in a reasonable period of time. Therefore, Tim has decided to switch from the basic EOQ model to the EOQ model with planned shortages, using a shortage cost of $$200$ per computer short per year. $($a$)$ find the new optimal inventory policy and its total variable inventory cost per year $($TVC$).$ What is the reduction in the value of TVC fornd for Prob. $18\mathrm{.}3-3($and given in the back of the bock$)$ when planned shortages were not allowed?