# Demand for calendars probability of demand 75000 015

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Chapter 1 / Exercise 4
Mathematical Applications for the Management, Life, and Social Sciences
Harshbarger
Expert Verified
Demand for Calendars Probability of Demand 75,000 0.15 80,000 0.25 85,000 0.30 90,000 0.20 95,000 0.10
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Chapter 1 / Exercise 4
Mathematical Applications for the Management, Life, and Social Sciences
Harshbarger
Expert Verified
The Office of Tourism sells the calendars for \$12.95 each. The calendars cost Sue \$5 each. The salvage value is estimated to be \$0.50 per unsold calendar. Determine how many calendars Sue should order to maximize expected profits. Answer: Based on the information provided, a payoff table is developed to determine the expected profit with each possible order quantity. (All values are in thousands.)When 80,000 calendars are bought and 80,000 calendars are sold, Payoff = 80,000(\$12.95 \$5) = \$636,000 When 90,000 calendars are ordered and demand is for only 80,000 calendars, Payoff = 80,000(\$12.95 \$5) ((90,000 80,000) × (\$5 \$0.50)) = \$591,000 When 85,000 calendars are ordered but 95,000 calendars are demanded, Payoff = 85,000(1\$12.95 \$5) = \$675,750 Once we generate the expected profit for each of the possible order quantities, we select the order quantity with the highest expected profit. Therefore, an order amount of 85,000 calendars maximizes expected profits. 176.The Office of Tourism (Problem 18) has decided to heavily promote local events this year and anticipates more tourists this season. Sue has changed the probability of selling Demand Expected 75 80 85 90 95 Profit 75 596.25 596.25 596.25 596.25 596.25 596.250 Order 80 573.75 636 636 636 636 626.6625 Amount 85 551.25 613.5 675.75 675.75 675.75 641.5125 90 528.75 591 653.25 715.5 715.5 637.6875 95 506.25 568.5 630.75 693.00 755.25 621.4125
different quantities of calendars as shown. Given the new probabilities, determine how many calendars Sue should order to maximize expected profits. Demand for Calendars Probability of Demand 75,000 0.05 80,000 0.20 85,000 0.25 90,000 0.30 95,000 0.20 Answer: Based on the information provided, a payoff table is developed to determine the expected profit with each possible order quantity. (All values are in thousands.) Once we generate the expected profit for each of the possible order quantities, we select the order quantity with the highest expected profit. Therefore, an order amount of 90,000 calendars maximizes expected profits. 177.Given the following list of items, a)Calculate the annual usage cost of each item. b)Classify the items as A, B, or C. Item Annual Demand Ordering Cost (\$) Holding Cost (%) Unit Price (\$) 101 500 10 20 0.5 102 1500 10 30 0.2 103 5000 25 30 1 104 250 15 25 4.5 105 1500 35 35 1.2 201 10000 25 15 0.75 202 1000 10 20 1.35 203 1500 20 25 0.2 204 500 40 25 0.8 Demand Expected 75 80 85 90 95 Profit 75 596.25 596.25 596.25 596.25 596.25 596.250 Order 80 573.75 636 636 636 636 632.888 Amount 85 551.25 613.5 675.75 675.75 675.75 657.075 90 528.75 591 653.25 715.5 715.5 665.700 95 506.25 568.5 630.75 693.00 755.25 655.650
205 100 10 15 2.5 Answer: Item Annual Usage (\$) % of Total Dollars Cumulative % of Total Dollars Item Classification 201 7500 41.0% 41.0% A 103 5000 27.4% 68.4% A 105 1800 9.8% 78.2% B 202 1350 7.4% 85.6% B 104 1125 6.2% 91.8% B 204 400 2.2% 94.0% C 203 300 1.6% 95.6% C 102 300 1.6% 97.3% C 101 250 1.4% 98.6% C 205 250 1.4% 100.0% C Total 18275 100% 178.Using the information provided in Problem 20, a)Calculate the economic order quantity for each item. (Round to the nearest whole number.) b)Calculate the company’s maximum inventory investment throughout the year.c)Calculate the company’s average inventory level.Answer: a)Item Annual Demand Ordering Cost (\$) Holding Cost (%) Unit Price (\$) EOQ 101 500 10 20 0.5 316 102 1500 10 30 0.2 707 103 5000 25 30 1 913 104 250 15 25 4.5 82 105 1500 35 35 1.2 500 201 10000 25 15 0.75 2108 202 1000 10 20 1.35 272 203 1500 20 25 0.2 1095 204 500 40 25 0.8 447 205 100 10 15 2.5 73 b)
Item EOQ Product Cost 101 316 158.11 102 707 141.42 103 913 912.87 104 82 367.42 105 500 600.00 201 2108 1581.14 202 272 367.42 203 1095 219.09 204 447 357.77 205 73 182.57 Using the EOQ number times the unit cost, the company’s maximum inventory