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
Chapter11: Product Concepts, Branding, And Packaging
Section11.1: Gaga: Not Just A Lady
Problem 2VC
Related questions
Question
![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F93393323-dd38-4844-a442-0d7a2169ce68%2F35fa9eeb-b5fc-48eb-8480-12ea16b99879%2Fftwzu0q_processed.jpeg&w=3840&q=75)
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F93393323-dd38-4844-a442-0d7a2169ce68%2F35fa9eeb-b5fc-48eb-8480-12ea16b99879%2Fdcf6g4r_processed.jpeg&w=3840&q=75)
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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