Please show all the work and provide explanations! Thank you!…Please show all the work and provide explanations! Thank you! Question 1: Suppose you purchase a part from a supplier for a unit cost of $4 with which you 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. a) How many parts should you purchase each time you place an order? b) To satisfy annual demand, how many times per year will you place orders for this part? Question 2: Victor sells a line of upscale evening dresses in his boutique. He charges $300 per dress, and sales average 30 dresses per week. Currently, Victor orders a 10-week supply at a time from the manufacturer. He pays $150 per dress, and it takes two weeks to receive each delivery. Victor estimates his administrative cost of placing each order at $225. Because he estimates his cost of inventory at 20%, each dollar’s worth of idle inventory costs him $0.30 per year. a) Compute Victor’s total annual cost of ordering and carrying inventory.b) If he wishes to minimize his annual cost, how much should Victor order in each batch?c) What will be his annual cost?d) Compare the number of inventory turns under the current and proposed policies. Specifically, what is the number of inventory turns under the current policy?e) Compare the number of inventory turns under the current and proposed policies. Specifically, what is the number of inventory turns under the proposed policy? Question 3: Gourmet Coffee (GC) is a specialty coffee shop that sells roasted coffee beans. It buys green beans, roasts them in its shop, and then sells them to the consumer. GC estimates that it sells about 150,000 pounds of coffee per year. Green beans cost about $1.50 per pound. In addition, there is a shipping charge that GC pays its supplier according to the following schedule:Quantity ShippedShipping Cost per PoundLess than 10,000 pounds$0.17Less than 15,000 pounds$0.15More than 15,000 pounds$0.13GC estimates its cost of inventory at 15% per year. The administrative cost of placing an order (fax/phone/billing) and receiving the goods and so on is about $50 per order. In addition, to receive a shipment into its shop, GC rents a forklift truck for $350. a) What is the optimal order quantity of beans for GC?b) What is the total annual cost?c) GC is considering buying a forklift and building a ramp that will allow it to eliminate the rental cost of a forklift. GC will have to borrow money to finance this investment. If the life of the equipment is approximately five years, how much money should GC be willing to spend to buy a forklift and build a ramp?d) If the investment were made, what should be the optimal order policy for GC – in particular, what is the optimal order quantity? Please show all the work and provide explanations! Thank you! Engineering & TechnologyIndustrial EngineeringOperations Management MGT 71
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