QUESTION $1$

$($a$)$ Discuss Backorders in Inventory Management.

$($b$)$ Consider a single product with the following inventory data:

Annual demand $(D)=10000$

Ordering cost$(S)=50$

Holding cost per unit per year $(H)=2$

Shortage cost per unit per year $(P)=5$

Average daily demand $(d)=40$

Using appropriate Mathematical formulas, obtain:

$($i$)$ The EOQ with Shortages

$($ii$)$ The Optimal Cycle Time $($T$)$

$($iii$)$ The plots for the costs

$($iv$)$ The equation for the holding cost curve

$($v$)$ The Quantity when the holding cost and the ordering cost are the same

QUESTION $2$

Consider three products with the following inventory data:

$($a$)$ Using appropriate Mathematical formulas, obtain the EQQ for the products:

$($i$)$ With Discount

$($ii$)$ Without Discount

$($b$)$ Plot the curves for the Total Costs versus the Quantity for the products $($combined$)$