Suppose your firm purchases a $4 per unit part from a supplier. Your firm uses the part to assemble red widgets. On average, you use 50,000 units of this part each year. Every time you order this particular part, you incur a sizable ordering cost of $800 regardless of the number of parts you order. Your cost of capital is 20% per year and your unit holding cost per year is 10%.

1. How many parts should you purchase each time you place an order (i.e., what is the optimal order quantity)?

2. To satisfy annual demand, how many times per year will you place orders for this part if you order the optimal order quantity?

3. What is the total annual cost if you order the optimal order quantity (show your work)?

4. What is the total annual cost if you order 1,000 units instead of the optimal order quantity (show your work)?