$5.$ You have been tasked with developing the best ordering policy for the following two items, given that the company only wants to use an average of $4,500$ square feet of storage space. The manager of the company suggested you consider an additional cost factor C $=2.$ This additional cost factor is used to reduce the order size from EOQ in such a way that the average storage space constraint is respected.

Item

$1$

Unit Cost $($v$)$

Weekly Demand

Order Cost $($A$)$

Space per unit $($s$)($ft$^2)$

Holding Cost $\%$

S$9$

$$11\mathrm{.}5$

$600$

$$120$

$6$

$14\%$

$2$

$350$

$$110$

$1$

$8\%$

The company operates $50$ weeks per year.

a$.$ Is this a reasonable value for C$?$ Justify your answer.

b$.$ Assuming that we allocate $2400$ square feet and $2100$ square feet to items $1$ and $2,$ respectively. What would be your ordering policy recommendation for these items? For each item, explain how the TRC based on this new policy compares to the case with no space limitations$.$ Justify your answers.

$5.$

a$.$ No$,$ because it results in a total average space used that is less than the available space.

b$.$ The maximum space used by EOQ, exceeds the allocated space to item $1,$ therefore, the order quantity would be $400.$ The maximum space used by EOQ$2$ does not exceed the allocated space to item $2,$ therefore, the order quantity would be equal to EOQ$22045\mathrm{.}67.$

The TRC for item $1$ would be larger than the TRC for the setting with no space limitations $($the EOQ$),$ as the order quantity is different than EOQ. For Item $2,$ however, since the order quantity equals EOQ, the TRC remains the same as the case with no space limitations$.$