Tom's, Inc., produces varlous Mexican food products and sells them to Westem 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 chunkler 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 perlod, 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 Ingredlents Is approximately $0.10 per jar. Tom's, Inc., buys empty glass jars for $0.02 each, and labeling and nilling costs are estimated to be $0.03 for each jar of salsa produced, Tom's contract with WWestem Foods results lo 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 constralnts are ounces): Max 1W + 1.25M s.t. SW + 7M 3W + 1M 2W + 2M W, M20 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 Constraint Siack/Surplus Dual Value 0.00000 0.12500
Tom's, Inc., produces varlous Mexican food products and sells them to Westem 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 chunkler 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 perlod, 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 Ingredlents Is approximately $0.10 per jar. Tom's, Inc., buys empty glass jars for $0.02 each, and labeling and nilling costs are estimated to be $0.03 for each jar of salsa produced, Tom's contract with WWestem Foods results lo 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 constralnts are ounces): Max 1W + 1.25M s.t. SW + 7M 3W + 1M 2W + 2M W, M20 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 Constraint Siack/Surplus Dual Value 0.00000 0.12500
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Transcribed Image Text:Tom's, Inc., produces varlous Mexican food products and sells them to Westem Foods, a chain of grocery stores located In Texas and New Mexico, Tom's, Inc., makes two salsa products: Western Foods
Salsa and Medco 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 chunkler 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 ingredlents 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 constralnts are ounces):
Max 1W + 1.25M
s.t.
SW + 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
Constraint
Slack/Surplus
Dual Value
1
0.00000
0.12500
240.00000
0.00000
0.00000
0.18750
Objective
Coefficient
Allowable
Increase
Allowable
Docrease
Variable
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
Transcribed Image Text:(a) What is the optimal solution, and what are the optimal production quantities?
jars
jars
profit
(b) Specily the objective function ranges. (Round your answers to five decimal places.)
Westem 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 cunce 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 wil 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 Addtional ounces of tomato sauce wil 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.
OAdditional ounces of tomato paste wil not improve profts.
(d) Identify each of the right-hand-side renges. (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
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