# MAT540 Homework Week 9

MAT540 Homework Week 9

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MAT540

Week 9 Homework

Chapter 16

1. The Western Jeans Company purchases denim from Cumberland Textile Mills. The Western Jeans Company uses 35,000 yards of denim per year to make jeans. The cost of ordering denim from the textile company is $500 per order. It costs Western $0.35 per yard annually to hold a yard of denim in inventory. Determine the optimal number of yards of denim the Western Jeans Company should order, the minimum total annual inventory cost, the optimal number of orders per year, and the optimal time between orders.

2. The Metropolitan Book Company purchases paper from the Atlantic Paper Company. Metropolitan produces magazines and paperbacks that require 1,215,000 pounds of paper per year. The cost per order for the company is $1,200; the cost of holding 1 pound of paper in inventory is $0.08 per year. Determine the following: a) The economic order quantity b) The minimum total annual cost c) The optimal number of orders per year d) The optimal time between orders

3. The Petroco Company uses a highly toxic chemical in one of its manufacturing processes. It must have the product delivered by special cargo trucks designed for safe shipment of chemicals. As such, ordering (and delivery) costs are relatively high, at $2,600 per order. The chemical product is packaged in 1-gallon plastic containers. The cost of holding the chemical in storage is $50 per gallon per year. The annual demand for the chemical, which is constant over time, is 2,000 gallons per year. The lead time from time of order placement until receipt is 10 days. The company operates 310 working days per year. Compute the optimal order quantity, the total minimum inventory cost, and the reorder point.

4. The I-75 Carpet Discount Store has an annual demand of 10,000 yards of Super Shag carpet.

The annual carrying cost for a yard of this carpet is $0.75, and the ordering cost is $150. The carpet manufacturer normally charges the store $8 per yard for the carpet; however, the manufacturer has offered a discount price of $6.50 per yard if the store will order 5,000 yards. How much should the store order, and what will be the total annual inventory cost for that order quantity?

5. The office manager for the Gotham Life Insurance Company orders letterhead stationery from an office products firm in boxes of 500 sheets. The company uses 6,500 boxes per year. Annual carrying costs are $3 per box, and ordering costs are $28. The following discount price schedule is provided by the office supply company:

Order Quantity (in boxes) Price per Box 200-999 $16 1000-2999 14 3000-5999 13 6000+ 12

a. Determine the optimal order quantity and the total annual inventory cost. b. Determine the optimal order quantity and total annual inventory cost for boxes of stationery

if the carrying cost is 20% of the price of a box of stationery.