(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 to to to

MARKETING 2018
19th Edition
ISBN:9780357033753
Author:Pride
Publisher:Pride
Chapter12: Developing And Managing Products
Section12.1: Sriracha Heats Up The Hot Sauce Market
Problem 3VC
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Please only answer Part D

(a) What is the optimal solution, and what are the optimal production quantities?
W
M
profit
(b) Specify the objective function ranges. (Round your answers to five decimal places.)
Western Foods Salsa
Mexico City Salsa
jars
jars
(c) What are the dual values for each constraint? Interpret each.
constraint 1
One additional ounce of whole tomatoes will improve profits by $400.00.
One additional ounce of whole tomatoes will improve profits by $0.125.
One additional ounce of whole tomatoes will improve profits by $0.188.
Additional ounces of whole tomatoes will not improve profits.
constraint 2
One additional ounce of tomato sauce will improve profits by $400.00.
One additional ounce of tomato sauce will improve profits by $0.125.
One additional ounce of tomato sauce will improve profits by $0.188.
Additional ounces of tomato sauce will not improve profits.
constraint 3
One additional ounce of tomato paste will improve profits by $400.00.
One additional ounce of tomato paste will improve profits by $0.125.
One additional ounce of tomato paste will improve profits by $0.188.
Additional ounces of tomato paste will not improve profits.
constraint 1
(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 2
constraint 3
to
to
to
to
to
Transcribed Image Text:(a) What is the optimal solution, and what are the optimal production quantities? W M profit (b) Specify the objective function ranges. (Round your answers to five decimal places.) Western Foods Salsa Mexico City Salsa jars jars (c) What are the dual values for each constraint? Interpret each. constraint 1 One additional ounce of whole tomatoes will improve profits by $400.00. One additional ounce of whole tomatoes will improve profits by $0.125. One additional ounce of whole tomatoes will improve profits by $0.188. Additional ounces of whole tomatoes will not improve profits. constraint 2 One additional ounce of tomato sauce will improve profits by $400.00. One additional ounce of tomato sauce will improve profits by $0.125. One additional ounce of tomato sauce will improve profits by $0.188. Additional ounces of tomato sauce will not improve profits. constraint 3 One additional ounce of tomato paste will improve profits by $400.00. One additional ounce of tomato paste will improve profits by $0.125. One additional ounce of tomato paste will improve profits by $0.188. Additional ounces of tomato paste will not improve profits. constraint 1 (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 2 constraint 3 to to to to to
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
jars of Mexico City Salsa
leads to the formulation (units for constraints are ounces):
Max 1W + 1.25M
s.t.
M
=
5W + 7M
3W + 1M
2W + 2M
W, M ≥ 0
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
Value
520.00000
280.00000
oz of whole tomatoes
oz of tomato sauce
oz of tomato paste
Slack/Surplus
0.00000
400.00000
0.00000
1.00000
1.25000
Reduced Cost
0.00000
0.00000
RHS
Value
Objective Allowable
Coefficient
Increase
4560.00000
2240.00000
1600.00000
Dual Value
0.12500
0.00000
0.18750
0.25000
0.15000
Allowable
Increase
1040.00000
Infinite
100.00000
Allowable
Decrease
0.10714
0.25000
Allowable
Decrease
400.00000
400.00000
297.14286
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, 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 jars of Mexico City Salsa leads to the formulation (units for constraints are ounces): Max 1W + 1.25M s.t. M = 5W + 7M 3W + 1M 2W + 2M W, M ≥ 0 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 Value 520.00000 280.00000 oz of whole tomatoes oz of tomato sauce oz of tomato paste Slack/Surplus 0.00000 400.00000 0.00000 1.00000 1.25000 Reduced Cost 0.00000 0.00000 RHS Value Objective Allowable Coefficient Increase 4560.00000 2240.00000 1600.00000 Dual Value 0.12500 0.00000 0.18750 0.25000 0.15000 Allowable Increase 1040.00000 Infinite 100.00000 Allowable Decrease 0.10714 0.25000 Allowable Decrease 400.00000 400.00000 297.14286
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