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

$\backslash [$

$\backslash$begin$\{$array$\}\{$l$\}$

Q$^\{*\}=3\backslash$overleftarrow$\{3\}\backslash \backslash$

T C$=\backslash$$ $549\mathrm{.}91$

$\backslash$end$\{$array$\}$

$\backslash ]$

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

$\backslash [$

$\backslash$begin$\{$aligned$\}$

Q$^\{*\}$ & $=$ & $]\backslash$times $\backslash \backslash$

T C & $=\backslash$$ & $\backslash$times

$\backslash$end$\{$aligned$\}$

$\backslash ]$

$]$ X 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 and 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.

$($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.$)$