Question $1$

As the convenience store operations manager, you are required to manage the inventory for the paper cup. Your estimation of the annual demand of the product is $18,000$ units. The original price from the supplier is $$30$ per unit.

The ordering cost per order is $$25$ and the holding cost is $10\%$ per unit price per unit per year. The delivery lead time is $2$ working days. There are $250$ working days a year. All assumptions of the Economic Order Quantity $($EOQ$)$ model are satisfied. Show the units and steps of your calculation when you answer the following questions.

a$)$ Calculate the EOQ without discount. $($round up to integer$)$

b$)$ Calculate the total annual cost without discount, which is the sum of annual product cost, annual holding cost and annual ordering cost. $($correct to $1$ decimal place$)$

c$)$ Determine the reorder point $($ROP$).$

Facing the difficult time to run the business, you asked the supplier for discount. After negotiating, the paper cup supplier agreed to give you the quantity discount as shown in Table Q$1.$

Facing the difficult time to run the business, you asked the supplier for discount. After

negotiating, the paper cup supplier agreed to give you the quantity discount as shown in

Table Q$1.$

Table Q$1$d$)$ The price of the item is a factor in holding cost, the holding cost changes as the price

changes. Calculate the holding cost per unit per year for discount price $1.$

$($correct to $1$ decimal place$)$

e$)$ Calculate the EOQ for discount price $1.$

f$)$ Calculate the total annual cost for discount price $1,$ which is the sum of annual product cost annual holding cost and annual ordering cost.