The A&M Hobby Shop carries a line of radio$-$controlled model racing cars. Demand for the cars is assumed to be constant at a rate of $50$ cars per month. The cars cost $$80$ each, and ordering costs are approximately $$15$ per order, regardless of the order size. The annual holding cost rate is $20\%.$

$($a$)$ Determine the economic order quantity and total annual cost $($in $$)$ under the assumption that no backorders are permitted. $($Round your answers to two decimal places.$)$

$Q^{**}=$

$TC=$$

$($b$)$ Using a $$45$ per$-$unit per$-$year backorder cost, determine the minimum cost inventory policy and total annual cost $($in $ $)$ for the model racing cars. $($Round your answers to two decimal places.$)$

$Q^{**}=$

$TC=$$

$($c$)$ What is the maximum number of days a customer would have to wait for a backorder under the policy in part $($b$)?$ Assume that the Hobby Shop is open for business $300$ days per year. $($Round your answer to two decimal places.$)$ days

$($d$)$ Would you recommend a no$-$backorder or a backorder inventory policy for this product? Explain.

Yes, the maximum wait is less than a week and the backorder case has a lower cost than the EOQ case.

Yes, the maximum wait is over a week long, but the cost savings of the backorder case is large enough to justify a long wait.

No$,$ the maximum wait is less than a week but the EOQ case has a lower cost than the backorder case.

No$,$ the maximum wait is over a week long, which does not justify the cost savings of the backorder case.

No$,$ the maximum wait is over a week long and the EOQ case has a lower cost than the backorder case.

$($e$)$ If the lead time is six days, what is the reorder point for both the no$-$backorder and backorder inventory policies? $($Round your answers to two decimal places.$)$

EOQ $r=$

Backorder $r=$