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, 150 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. SW + 7M 3W + 1M 2W + 2M W, M 20 The computer solution is shown below. profit Variable W M Optimal Objective Value - 870.00000 Constraint 1 2 3 Variable W M s 4,560 $ 2,400 ≤ 1,600 Constraint 1 2 3 280 $ 870 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 560.00000 0.00000 1.00000 1.25000 Objective Allowable Allowable Coefficient Increase Decrease 0.25000 0.15000 Dual Value 0.12500 0.00000 0.18750 RHS Value 4560.00000 1040.00000 Allowable Increase 2400.00000 1600.00000 ✔jars ✔jars 0.10714 0.25000 (a) What is the optimal solution, and what are the optimal production quantities? 520 W M Allowable Decrease 560.00000 560.00000 Infinite 140.00000 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, 150 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. SW + 7M 3W + 1M 2W + 2M W, M 20 The computer solution is shown below. profit Variable W M Optimal Objective Value - 870.00000 Constraint 1 2 3 Variable W M s 4,560 $ 2,400 ≤ 1,600 Constraint 1 2 3 280 $ 870 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 560.00000 0.00000 1.00000 1.25000 Objective Allowable Allowable Coefficient Increase Decrease 0.25000 0.15000 Dual Value 0.12500 0.00000 0.18750 RHS Value 4560.00000 1040.00000 Allowable Increase 2400.00000 1600.00000 ✔jars ✔jars 0.10714 0.25000 (a) What is the optimal solution, and what are the optimal production quantities? 520 W M Allowable Decrease 560.00000 560.00000 Infinite 140.00000 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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Question
Transcribed Image Text:profit $ 870
(b) Specify the objective function ranges. (Round your answers to five decimal places.)
Western Foods Salsa
Mexico City Salsa
1.25000
140000
(c) What are the dual values for each constraint? Interpret each.
constraint 1
constraint 2
Xto 0.89286
X to 1.00000
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 $560.00.
O Additional ounces of whole tomatoes will not improve profits.
constraint 3
X
X
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 $560.00.
Additional ounces of tomato sauce will not improve profits.
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.
O One additional ounce of tomato paste will improve profits by $560.00.
O Additional ounces of tomato paste will not improve profits.
to
to
to
(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
constraint 2
constraint 3
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 285 pounds of whole tomatoes, 150 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
Optimal Objective Value = 870.00000
M
Constraint
1
2
3
Variable
≤ 4,560
≤ 2,400
≤ 1,600
W
M
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
560.00000
0.00000
1.00000
1.25000
Objective Allowable Allowable
Coefficient
Decrease
Increase
0.25000
0.15000
RHS
Value
Dual Value
0.12500
0.00000
0.18750
4560.00000
2400.00000
1600.00000
0.10714
0.25000
Allowable Allowable
Increase
Decrease
1040.00000
560.00000
560.00000
297.14286
Infinite
140.00000
(a) What is the optimal solution, and what are the optimal production quantities?
W
520
✔ jars
M
280
✔ jars
profit
$ 870
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