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(a) What is the optimal solution, and what are the optimal production quantities? W M profit $ jars jars (b) Specify the objective function ranges. (Round your answers to five decimal places.) Western Foods Salsa to Mexico City Salsa to (c) What are the dual values for each constraint? Interpret each. constraint 1 One additional ounce of whole tomatoes will improve profits by $0.125. O One additional ounce of whole tomatoes will improve profits by $0.188. O One additional ounce of whole tomatoes will improve profits by $240.00. Additional ounces of whole tomatoes will not improve profits. constraint 2 One additional ounce of tomato sauce will improve profits by $0.125. One additional ounce of tomato sauce will improve profits by $0.188.

(a) What is the optimal solution, and what are the optimal production quantities? W M profit $ jars jars (b) Specify the objective function ranges. (Round your answers to five decimal places.) Western Foods Salsa to Mexico City Salsa to (c) What are the dual values for each constraint? Interpret each. constraint 1 One additional ounce of whole tomatoes will improve profits by $0.125. O One additional ounce of whole tomatoes will improve profits by $0.188. O One additional ounce of whole tomatoes will improve profits by $240.00. Additional ounces of whole tomatoes will not improve profits. constraint 2 One additional ounce of tomato sauce will improve profits by $0.125. One additional ounce of tomato sauce will improve profits by $0.188.

Practical Management Science
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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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 275 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. < 4,400 < 2,240 < 1,600 5W + 7M oz of whole tomatoes 3W + 1M oz of tomato sauce oz of tomato paste 2W + 2M W, M 2 0 The computer solution is shown below. Optimal Objective Value 850.00000 Variable Value Reduced Cost W 600.00000 0.00000 M 200.00000 0.00000 Constraint Slack/Surplus Dual Value 1 0.00000 0.12500 240.00000 0.00000 0.00000 0.18750 Objective Allowable Allowable Variable Coefficient Increase Decrease W 1.00000 0.25000 0.10714 M 1.25000 0.15000 0.25000 RHS Allowable Allowable Constraint Value Increase Decrease 1 4400.00000 1200.00000 240.00000 2240.00000 Infinite 240.00000 3 1600.00000 60.00000 342.85714 (a) What is the optimal solution, and what are the optimal production quantities? W jars
Transcribed Image Text: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 275 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. < 4,400 < 2,240 < 1,600 5W + 7M oz of whole tomatoes 3W + 1M oz of tomato sauce oz of tomato paste 2W + 2M W, M 2 0 The computer solution is shown below. Optimal Objective Value 850.00000 Variable Value Reduced Cost W 600.00000 0.00000 M 200.00000 0.00000 Constraint Slack/Surplus Dual Value 1 0.00000 0.12500 240.00000 0.00000 0.00000 0.18750 Objective Allowable Allowable Variable Coefficient Increase Decrease W 1.00000 0.25000 0.10714 M 1.25000 0.15000 0.25000 RHS Allowable Allowable Constraint Value Increase Decrease 1 4400.00000 1200.00000 240.00000 2240.00000 Infinite 240.00000 3 1600.00000 60.00000 342.85714 (a) What is the optimal solution, and what are the optimal production quantities? W jars
(a) What is the optimal solution, and what are the optimal production quantities? W jars M jars profit (b) Specify the objective function ranges. (Round your answers to five decimal places.) Western Foods Salsa to Mexico City Salsa to (c) What are the dual values for each constraint? Interpret each. constraint 1 One additional ounce of whole tomatoes will improve profits by $0.125. One additional ounce of whole tomatoes will improve profits by $0.188. One additional ounce of whole tomatoes will improve profits by $240.00. Additional ounces of whole tomatoes will not improve profits. constraint 2 One additional ounce of tomato sauce will improve profits by $0.125. One additional ounce of tomato sauce will improve profits by $0.188. One additional ounce of tomato sauce will improve profits by $240.00. Additional ounces of tomato sauce will not improve profits. constraint 3 One additional ounce of tomato paste will improve profits by $0.125. One additional ounce of tomato paste will improve profits by $0.188. One additional ounce of tomato paste will improve profits by $240.00. Additional ounces of tomato paste will not improve profits. (d) Identify each of the right-hand-side ranges. (Round your answers to two decimal places. If there is no upper or lower limit, enter NO LIMIT.) constraint 1 to constraint 2 to constraint 3 to O O O O O O O O
Transcribed Image Text:(a) What is the optimal solution, and what are the optimal production quantities? W jars M jars profit (b) Specify the objective function ranges. (Round your answers to five decimal places.) Western Foods Salsa to Mexico City Salsa to (c) What are the dual values for each constraint? Interpret each. constraint 1 One additional ounce of whole tomatoes will improve profits by $0.125. One additional ounce of whole tomatoes will improve profits by $0.188. One additional ounce of whole tomatoes will improve profits by $240.00. Additional ounces of whole tomatoes will not improve profits. constraint 2 One additional ounce of tomato sauce will improve profits by $0.125. One additional ounce of tomato sauce will improve profits by $0.188. One additional ounce of tomato sauce will improve profits by $240.00. Additional ounces of tomato sauce will not improve profits. constraint 3 One additional ounce of tomato paste will improve profits by $0.125. One additional ounce of tomato paste will improve profits by $0.188. One additional ounce of tomato paste will improve profits by $240.00. Additional ounces of tomato paste will not improve profits. (d) Identify each of the right-hand-side ranges. (Round your answers to two decimal places. If there is no upper or lower limit, enter NO LIMIT.) constraint 1 to constraint 2 to constraint 3 to O O O O O O O O
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