Tom's, Inc., produces various Mexican food products and sells them to Western Foods, a chain of grocery stores located in Texas and New Mexico. Tom's, Inc., makes two salsa products: Western Foods Salsa and Mexico City Salsa. Essentially, the two products have different blends of whole tomatoes, tomato sauce, and tomato paste. The Western Foods Salsa is a blend of 50% whole tomatoes, 30% tomato sauce, and 20% tomato paste. The Mexico City Salsa, which has a thicker and chunkier consistency, consists of 70% whole tomatoes, 10% tomato sauce, and 20% tomato paste. Each jar of salsa produced weighs 10 ounces. For the current production period, Tom's, Inc., can purchase up to 285 pounds of whole tomatoes, 140 pounds of tomato sauce, and 100 pounds of tomato paste; the price per pound for these ingredients is $0.96, $0.64, and $0.56, respectively. The cost of the spices and the other ingredients is approximately $0.10 per jar. Tom's, Inc., buys empty glass jars for $0.02 each, and labeling and filling costs are estimated to be $0.03 for each jar of salsa produced. Tom's contract with Western Foods results in sales revenue of $1.64 for each jar of Western Foods Salsa and $1.93 for each jar of Mexico City Salsa. Letting W = jars of Western Foods Salsa M = jars of Mexico City Salsa leads to the formulation (units for constraints are ounces): Max 1W+1.25M s.t. 5W + 7M 3W + 1M 2W + 2M W, M 20 The computer solution is shown below. Variable W M Optimal Objective Value = 870.00000 Constraint 1 2 3 Variable W M ≤ 4,560 ≤ 2,240 ≤ 1,600 Constraint 1 2 3 oz of whole tomatoes oz of tomato sauce oz of tomato paste Value Reduced Cost 0.00000 0.00000 520.00000 280.00000 Slack/Surplus 0.00000 400.00000 0.00000 1.00000 1.25000 Objective Allowable Allowable Coefficient Increase Decrease 0.10714 0.25000 Dual Value 0.12500 0.00000 0.18750 RHS Value 0.25000 0.15000 Allowable Increase 4560.00000 1040.00000 2240.00000 Infinite 1600.00000 100.00000 Allowable Decrease 400.00000 400.00000 297.14286
Tom's, Inc., produces various Mexican food products and sells them to Western Foods, a chain of grocery stores located in Texas and New Mexico. Tom's, Inc., makes two salsa products: Western Foods Salsa and Mexico City Salsa. Essentially, the two products have different blends of whole tomatoes, tomato sauce, and tomato paste. The Western Foods Salsa is a blend of 50% whole tomatoes, 30% tomato sauce, and 20% tomato paste. The Mexico City Salsa, which has a thicker and chunkier consistency, consists of 70% whole tomatoes, 10% tomato sauce, and 20% tomato paste. Each jar of salsa produced weighs 10 ounces. For the current production period, Tom's, Inc., can purchase up to 285 pounds of whole tomatoes, 140 pounds of tomato sauce, and 100 pounds of tomato paste; the price per pound for these ingredients is $0.96, $0.64, and $0.56, respectively. The cost of the spices and the other ingredients is approximately $0.10 per jar. Tom's, Inc., buys empty glass jars for $0.02 each, and labeling and filling costs are estimated to be $0.03 for each jar of salsa produced. Tom's contract with Western Foods results in sales revenue of $1.64 for each jar of Western Foods Salsa and $1.93 for each jar of Mexico City Salsa. Letting W = jars of Western Foods Salsa M = jars of Mexico City Salsa leads to the formulation (units for constraints are ounces): Max 1W+1.25M s.t. 5W + 7M 3W + 1M 2W + 2M W, M 20 The computer solution is shown below. Variable W M Optimal Objective Value = 870.00000 Constraint 1 2 3 Variable W M ≤ 4,560 ≤ 2,240 ≤ 1,600 Constraint 1 2 3 oz of whole tomatoes oz of tomato sauce oz of tomato paste Value Reduced Cost 0.00000 0.00000 520.00000 280.00000 Slack/Surplus 0.00000 400.00000 0.00000 1.00000 1.25000 Objective Allowable Allowable Coefficient Increase Decrease 0.10714 0.25000 Dual Value 0.12500 0.00000 0.18750 RHS Value 0.25000 0.15000 Allowable Increase 4560.00000 1040.00000 2240.00000 Infinite 1600.00000 100.00000 Allowable Decrease 400.00000 400.00000 297.14286
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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