Demand for the PCPro computer at the retailer B$-$Buy is $1,000$ units per month. B$-$Buy incurs a fixed order placement, transportation, and receiving cost of $$2,000$ each time an order is placed. Each computer costs $$600$ for B$-$Buy, and the retailer, operating in a highly inflationary market, has a holding cost rate of $27\%.$ The delivery lead time is six days. $($Assume $30$ days in a month.$)$ Currently, B$-$Buy is ordering every two months.

a$)$For the current inventory policy, calculate the reorder point and the total cost of operating this policy $($i$.$e$.,$ the sum of inventory holding and ordering costs per year.$).$

B$)$Draw the corresponding inventory$-$time diagram and explain how the current inventory system operates in two sentences.

c$)$Assume B$-$Buy hired an MBA student named John, who thinks an EOQ approach would be appropriate. Do you agree? Why, why not?

d$)$ John further claims that by ordering at the EOQ $($call this proposed inventory policy$),$ the total inventory costs will be almost halved, resulting in substantial cost savings. Show, quantitatively, if John is correct or not.

E$)$The store manager at B$-$Buy would like the optimal lot size to be $500.$ For this to happen, calculate how much the order cost per lot should be reduced.