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Max 1W + 1.25M s.t. 5W + 7M 3W + 1M 2W + 2M W, M 20 S 4,400 S 2,240 S 1,600 oz of whole tomatoes oz of tomato sauce oz of tomato paste The computer solution is shown below. Optimal Objective Value - 850.00000 Variable Value Reduced Cost 600.00000 0.00000 200.00000 0.00000 Slack/Surplus 0.00000 Constraint Dual Value 1. 0.12500 2. 240.00000 0.00000 3. 0.00000 0.18750 Objective Coefficient Allowable Increase Allowable Variable Decrease 1.00000 0.25000 0.10714 1.25000 0.15000 0.25000 Constraint RHS Allowable Allowable Value Increase Decrease 4400.00000 1200.00000 240.00000 2 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? |jars 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 O One additional ounce of whole tomatoes will improve profits by $0.125. 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 O One additional ounce of tomato sauce will improve profits by $0.125. O One additional ounce of tomato sauce will improve profits by $0.188. O One additional ounce of tomato sauce will improve profits by $240.00. O Additional ounces of tomato sauce will not improve profits. constraint 3 O One additional ounce of tomato paste will improve profits by $0.125. O One additional ounce of tomato paste will improve profits by $0.188. O One additional ounce of tomato paste will improve profits by $240.00. O 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

Max 1W + 1.25M s.t. 5W + 7M 3W + 1M 2W + 2M W, M 20 S 4,400 S 2,240 S 1,600 oz of whole tomatoes oz of tomato sauce oz of tomato paste The computer solution is shown below. Optimal Objective Value - 850.00000 Variable Value Reduced Cost 600.00000 0.00000 200.00000 0.00000 Slack/Surplus 0.00000 Constraint Dual Value 1. 0.12500 2. 240.00000 0.00000 3. 0.00000 0.18750 Objective Coefficient Allowable Increase Allowable Variable Decrease 1.00000 0.25000 0.10714 1.25000 0.15000 0.25000 Constraint RHS Allowable Allowable Value Increase Decrease 4400.00000 1200.00000 240.00000 2 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? |jars 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 O One additional ounce of whole tomatoes will improve profits by $0.125. 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 O One additional ounce of tomato sauce will improve profits by $0.125. O One additional ounce of tomato sauce will improve profits by $0.188. O One additional ounce of tomato sauce will improve profits by $240.00. O Additional ounces of tomato sauce will not improve profits. constraint 3 O One additional ounce of tomato paste will improve profits by $0.125. O One additional ounce of tomato paste will improve profits by $0.188. O One additional ounce of tomato paste will improve profits by $240.00. O 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

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter4: Linear Programming Models
Section: Chapter Questions
Problem 77P
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leads to the formulation (units for constraints are ounces): Max 1W + 1.25M s.t. 5W + 7M 3W + 1M 2W + 2M W, M 20 S 4,400 S 2,240 s 1,600 oz of whole tomatoes oz of tomato sauce oz of tomato paste 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 2 240.00000 0.00000 3 0.00000 0.18750 Objective Coefficient Allowable Allowable Variable 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? jars 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 O 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. O Additional ounces of whole tomatoes will not improve profits. constraint 2 O One additional ounce of tomato sauce will improve profits by $0.125. O One additional ounce of tomato sauce will improve profits by $0.188. O One additional ounce of tomato sauce will improve profits by $240.00. O Additional ounces of tomato sauce will not improve profits. constraint 3 O 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. O 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
Transcribed Image Text:leads to the formulation (units for constraints are ounces): Max 1W + 1.25M s.t. 5W + 7M 3W + 1M 2W + 2M W, M 20 S 4,400 S 2,240 s 1,600 oz of whole tomatoes oz of tomato sauce oz of tomato paste 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 2 240.00000 0.00000 3 0.00000 0.18750 Objective Coefficient Allowable Allowable Variable 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? jars 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 O 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. O Additional ounces of whole tomatoes will not improve profits. constraint 2 O One additional ounce of tomato sauce will improve profits by $0.125. O One additional ounce of tomato sauce will improve profits by $0.188. O One additional ounce of tomato sauce will improve profits by $240.00. O Additional ounces of tomato sauce will not improve profits. constraint 3 O 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. O 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
Tom's, Inc., produces various Mexican food products änd šēlls thêm tô 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. estern FOods, a or grocery stores 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. 5W + 7M 3W + 1M S 4,400 S 2,240 s 1,600 oz of whole tomatoes oz of tomato sauce oz of tomato paste 2W + 2M W, M 20 The computer solution is shown below. Optimal Objective Value - 850.00000 Variable Value Reduced Cost 600.00000 0.00000 M 200.00000 0.00000 Constraint Slack/Surplus Dual Value 0.00000 0.12500 240.00000 0.00000 3 0.00000 0.18750 Objective Coefficient Allowable Allowable Variable Increase Decrease 1.00000 0.25000 0.10714 1.25000 0.15000 0.25000 RHS Allowable Allowable Constraint Value Increase Decrease 4400.00000 1200.00000 240.00000 2. 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? jars jars profit 24 (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 O 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. O One additional ounce of tomato sauce will improve profits by $0.188. O One additional ounce of tomato sauce will improve profits by $240.00. O Additional ounces of tomato sauce will not improve profits. constraint 3 O One additional ounce of tomato paste will improve profits by $0.125.
Transcribed Image Text:Tom's, Inc., produces various Mexican food products änd šēlls thêm tô 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. estern FOods, a or grocery stores 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. 5W + 7M 3W + 1M S 4,400 S 2,240 s 1,600 oz of whole tomatoes oz of tomato sauce oz of tomato paste 2W + 2M W, M 20 The computer solution is shown below. Optimal Objective Value - 850.00000 Variable Value Reduced Cost 600.00000 0.00000 M 200.00000 0.00000 Constraint Slack/Surplus Dual Value 0.00000 0.12500 240.00000 0.00000 3 0.00000 0.18750 Objective Coefficient Allowable Allowable Variable Increase Decrease 1.00000 0.25000 0.10714 1.25000 0.15000 0.25000 RHS Allowable Allowable Constraint Value Increase Decrease 4400.00000 1200.00000 240.00000 2. 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? jars jars profit 24 (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 O 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. O One additional ounce of tomato sauce will improve profits by $0.188. O One additional ounce of tomato sauce will improve profits by $240.00. O Additional ounces of tomato sauce will not improve profits. constraint 3 O One additional ounce of tomato paste will improve profits by $0.125.
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ISBN:
9781337406659
Author:
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