Shoplift Ltd$.$ expects to sell $120$ units, per day, of line item ELECT$123$Z in the next financial year $($assume $360$ trading days in year$).$

$$ The cost price per unit is R$62\mathrm{.}50$

$$ Shoplift Ltd$.$ is very concerned about holding too much inventory. Accordingly the firm currently maintains an average inventory level $($A$)$ of just $500$ units.

$$ The fixed ordering cost for item ELECT$123$Z is R$1800$ per order $($regardless of quantity$).$

$$ Other costs currently include:

$$ Opportunity cost: R$?($to be calculated$)$

$$ Annual storage costs per unit: R $5\mathrm{.}63$ per unit.

$$ Annual inventory insurance cost: R$3\mathrm{.}13$ per unit.

$$ Annual depreciation and obsolescence cost: R$4\mathrm{.}38$ per unit.

$$ Cost of capital: $19\mathrm{.}50\%$

$$ Consideration must be given to the lead$-$time, from order to delivery, of $8$ days.

$$ The supplier of line item ELECT$123$Z is willing to give a discount of R$0\mathrm{.}15$ on the price if more than $3000$ units are ordered at a time and a discount of R$0\mathrm{.}30$ if more than $5000$ units are ordered at a time.

$3\mathrm{.}1$ Calculate the total inventory cost $($TIC$)$ that Shoplift Ltd$.$ currently pays for maintaining an average inventory level of $500$ units.

$3\mathrm{.}2$ How many orders must be placed annually based on the current average inventory level of $500$ units?

$3\mathrm{.}3$ Calculate the Economic Order Quantity $($EOQ$)$ that Shoplift Ltd$.$ should order if it wants to minimize its TIC.

$3\mathrm{.}4$ How many orders must be placed annually based on the EOQ?

$3\mathrm{.}5$ Calculate the total inventory cost $($TIC$)$ that Shoplift Ltd$.$ would pay if it ordered inventory based on the EOQ.

$3\mathrm{.}6$ Based on your answers above, would it be worthwhile to order the EOQ? Explain.

$3\mathrm{.}7$ Should any of the R$0\mathrm{.}15$ discount offer be considered? Explain in detail by comparing the TIC incurred when ordering $3000$ units to the TIC associated with ordering the EOQ as calculated in question $3\mathrm{.}3.$

$3\mathrm{.}8$ Should any of the R$0\mathrm{.}30$ discount offer be considered? Explain in detail by comparing the TIC incurred when ordering $5000$ units to the TIC associated with ordering the EOQ as calculated in question $3\mathrm{.}3.$