Your friend needs to purchase malt for his micro-brewery. His supplier charges $35 per delivery, for each delivery, regardless of the size of the order. The product cost your friend $1.20 per gallon. The annual holding cost per unit is assumed to be 35% of the item’s cost of $1.20. Assume that your friend’s weekly usage of malt is 250 gallons and the brewery is open 52 weeks per year.

a. Suppose your friend orders 2,500 gallons of malt each time an order is made. What is the total annual holding and ordering costs using this order quantity?

b. Suppose each order is for 500 gallons of malt, what is the total annual holding and ordering costs using this order quantity?

c. Use a data table to show how annual holding costs and annual ordering costs change as the order quantity Q changes. Start with a Q equal to 500 and increase Q in 500 unit increments up to 3000 (e.g., 500, 1000, 1500, 2000, 2500, and 3000). Produce a graph that shows the costs (ordering, holding, and total) by order quantity. Be sure to label your graph.

d. What should the order size be if your friend wants to minimize the annual sum of ordering and holding costs?

e. What would the cost per order (the ordering cost) need to be in order for a 500 gallon order to have annual holding and ordering costs of $900.00?

f. Consider 5 different demand scenarios where the demand rate is as follows: Scenario 1, demand = 0.25 of the original demand; Scenario2, demand = 0.5 of the original demand, Scenario 3, demand = original demand, Scenario 4, demand = 2 times the original demand; and Scenario 5, demand = 4 times the original demand. For each demand scenario find the EOQ and express the Annual EOQ costs as a % of the Annual Purchase Cost. Use the original ordering and holding costs inputs.

g. Suppose your friend’s supplier only accepts orders that are an integer multiple of 1,000 gallons. In other words, orders must be for 1,000 gallons, 2,000 gallons, 3,000 gallons, etc. but not 1,250 gallons or 2,600 gallons. What should your friend’s order quantity be to minimize ordering and holding costs? Show your analysis.

h. Suppose your friend’s malt supplier offers him a 5% discount if he is willing to purchase 8,000 gallons of malt or more each time an order is placed. Should your friend order enough malt to receive the discount? (Assume your friend has room to store the malt and the malt will not spoil). Show your analysis.

i. For what discount percentage is your friend indifferent between the two options—that is, determine the value of the discount percentage(currently 5%) for which total costs (holding costs + ordering costs + purchasing costs) are identical with and without the discount? Price discounts greater than this percentage make it advantageous to order the larger quantity to receive the reduced price. Price discount percentages below this amount means your friend is better off not accepting the discount.