Question $1$: An electronics retailer has a demand for $35$ laptop per month. The retailer incurs a fixed order placement, transportation, and receiving cost of $$150$ each time an order for laptops is placed with the manufacturer. The retailer incurs an annual holding cost of $30$ percent of the cost of the laptop. The manufacturer uses the following all unit discount pricing schedule. The retailer can only order in increments of $10.$ So$,$ the retailer can order $10$ or $20$ laptops, but it cannot order $15.$

Order Quantity

Unit Price

$0-100$

$$700$

$101-400$

$$650$

Greater than $401$

$$600$

$$

a$)$ What is the optimum lot size for the retailer? Use can Excel file to show all the possible lot sizes that the retailer can use to satisfy annual demand. For each possible lot size, calculate the annual holding cost, annual order cost, annual material cost, and total annual cost to select the optimum decision.

Optimum Lot Size $=390$

b$)$ What is the optimum cycle inventory?