Modeling Assignment 4

Question 1. At what order quantity is the maximum profit expected to occur given the probabilities for demand?

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Question 2. For a demand of 2000, what order quantity will result in a break-even profit? What will happen if more than this quantity is ordered? Hint: Use goal seek.

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Question 3. For what order quantity does the maximum profit occur when the probabilities for the possible demand values are all equal?

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Inputs Quality discount structure Ordering with Quantity Discounts Regular price $30.00 At least Unit cost Leftover price $10.00 $24.00 Sam's Bookstore, with many locations across the United states, places orders for all of the latest books and then distributes them 1000 $23.00 to its individual bookstores. Sam's needs a model to help it order the appropriate number of any title. For example, Sam's plans to Decision variable 2000 $22.25 order a popular new hardback novel, which it will sell for $30. It can purchase any number of this book from the publisher, but Order quantity 2500 3000 $21.75 due to quantity discounts, the unit cost for all books it order depends on the number ordered. 4000 $21.30 Uncertain variable If the number ordered is less than 1000, then the unit cost is $24. After each 1000, the unit cost (cost per book) drops to:$23 for at least 1000 copies; $22.25 for at least 2000 copies; $21.75 for at least 3000 copies; and $21.30 for at least 4000 copies. For Demand 2000 example, if sam's order 2500 books, its total cost is 2500*$22.25 = $55,625 Profit model Sam's is uncertain about the demand for this book - it estimates that demand could be anywhere from 500 to 4500. Also, as with Units sold at regular price 2000 most hardback novels, this one will eventually come out in paperback. Therefore, if sam's has any hardbacks left when the Units sold at leftover price 500 paperback comes out, it will put them on sale for $10, a price at which Sam's believes all the leftovers will be sold. Revenue $65,000.00 Cost $55,625.00 How many copies of this hardback should Sam's order from the publisher? Profit $9,375.00 Data table of profit as a function of order quantity (along side) and demand (along top]. $9,375.00 500 1000 1500 2000 2500 3,000.00 3500 4000 4500 500 $3,000.00 $3,000.00 $3,000.00 $3,000.00 $3,000.00 3,000.00 $3,000.00 $3,000.00 $3,000.00 1000 -$3,000.00 $7,000.00 $7,000.00 $7/000.00 $7/000.00 7/000.00 $7/000.00 $7/000.00 $7/000.00 1500 -$9,500.00 $500.00 $10,500.00 $10,500.00 $10,500.00 10,500.00 $10,500.00 #10,500.00 $10,500.00 2000 -$14,500.00 -$4,500.00 $5,500.00 $15,500.00 $15,500.00 15,500.00 $15,500.00 $15,500.00 $15,500.00 2500 -$20,625.00 -$10,625.00 $625.00 $9,375.00 $19,375.00 19,375.00 $19,375.00 $19,375.00 $19,375.00 3000 -$25,250.00 -$15,250.00 -$5,250.00 $4,750.00 $14,750.00 24,750.00 $24,750.00 $24,750.00 $24,750.00 3500 -$31,125.00 -$21,125.00 -$11,125.00 -$1,125.00 $8,875.00 18,875.00 $28,875.00 $28,875.00 $28,875.00 4000 -$35,200.00 -$25,200.00 -$15,200.00 -$5,200.00 $4.800.00 $24,800.00 $34,800.00 $34,800.00 4500 -$40,850.00 -$30,850.00 -$20,850.00 -$10,850.00 -$850.00 9,150.00 $19,150.00 $29,150.00 $39,150.00 Model of expected demands Demand 500 1000 1500 2000 2500 3,000.00 3500 4000 4500 Probability 0.025 0.05 D. 15 0.25 0.25 0.15 0.07 0.04 0.015 Order quantity Expected profit 500 3,000.00 Expected Profit versus Order Quantity 1000 6,750.00 12,250.00 1500 9,500.00 11,375.00 2000 12,250.00 9,500.00 9,500.00 2500 11,375.00 6,750.00 3000 9,500.00 500 4,875.00 4,875.00 1.350.00 Profit 4000 -3,000.00 4500 (4.150.00) 1,350.00 500 1500 20 00 2500 30 0D 3500 400O (4,150.00) Order Quantity