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 vith 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): Max1W + 1.25M s.t. Sw + 7M 3W + 1M 2W + 2M W. M 20 S 4,560 s 2,400 S 1,600 oz of whole tomatoes oz of tomato sauce oz of tomato paste The computer solution is shown below. Optimal Objective Value = 70.00000 Value Reduced Cons 520.00000 0.00000 280.00000 0.00000 Constrains Slack/Surplus Dual Value 0.00000 0.12500 S60.00000 0.00000 0.00000 0.18750 Allowable Increase Objective Allowable Variable Coefficient Decrease 1.00000 0.25000 0.10714 1.25000 0.15000 0.25000 RHS Allowable Allowable Constrains Value Inerease Decrease 4560.00000 1040.00000 SE0.00000 2400.00000 Infinite Se0.00000 1600.00000 140.00000 297.14206 (a) What is the optimal solution, and what are the optimal production quantities? jars )jars M 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 vill improve profits by $0.188. O One additional ounce of whole tomatoes vill improve profits by $560.00. O One additional ounce of whole tomatoes vill improve profits by $0.125. O Additional ounces of whole tomatoes will not improve profits. constraint 2 O One additional ounce of tomato sauce vill improve profits by $0.188. O One additional ounce of tomato sauce vill improve profits by $560.00. O One additional ounce of tomato sauce vill improve profits by $0.125. O Additional ounces of tomato sauce vill not improve profits. constraint 3 O One additional ounce of tomato paste vill improve profits by $0.188. O One additional ounce of tomato paste will improve profits by $560.00. One additional ounce of tomato paste will improve profits by $0.125. O Additional ounces of tomato paste vill not improve profits. (d) Identify each of the right-hand-side ranges. (Round your answers to tvo 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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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% vhole 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):
Max1W + 1.25M
s.t.
5W + 7M
3W + 1M
2W + 2M
w, M 2 0
S 4,560
s 2,400
s 1,600
oz of whole tomatoes
oz of tomato sauce
oz of tomato paste
The computer solution is shown below.
Optimal Objective Value = 870.00000
Variable
Value
Reduced Cost
520.00000
0.00000
280.00000
0.00000
Constraint
3lack/Surplus
Dual Value
0.00000
0.12500
2
560.00000
0.00000
3
0.00000
0.18750
Objective
Allowable
Allowable
Variable
Coefficient
Increase
Decrease
1.00000
0.25000
0.10714
1.25000
0.15000
0.25000
RH3
Allowable
Allowable
Constraint
Value
Increase
Decrease
4560.00000
1040.00000
560.00000
2400.00000
Infinite
560.00000
1600.00000
140.00000
297.14286
(a) What is the optimal solution, and what are the optimal production quantities?
jars
M
jars
profit
$4
(b) Specify the objective function ranges. (Round your answers to five decimal places.)
Western Foods Salsa
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 $0.188.
O One additional ounce of whole tomatoes will improve profits by $560.00.
O One additional ounce of whole tomatoes will improve profits by $0.125.
O Additional ounces of whole tomatoes will not improve profits.
constraint 2
O One additional ounce of tomato sauce will improve profits by $0.188.
O One additional ounce of tomato sauce will improve profits by $560.0o.
O One additional ounce of tomato sauce will improve profits by $0.125.
O Additional ounces of tomato sauce vill not improve profits.
constraint 3
O One additional ounce of tomato paste will improve profits by $0.188.
O One additional ounce of tomato paste will improve profits by $560.0o.
O One additional ounce of tomato paste will improve profits by $0.125.
O Additional ounces of tomato paste vill 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: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% vhole 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): Max1W + 1.25M s.t. 5W + 7M 3W + 1M 2W + 2M w, M 2 0 S 4,560 s 2,400 s 1,600 oz of whole tomatoes oz of tomato sauce oz of tomato paste The computer solution is shown below. Optimal Objective Value = 870.00000 Variable Value Reduced Cost 520.00000 0.00000 280.00000 0.00000 Constraint 3lack/Surplus Dual Value 0.00000 0.12500 2 560.00000 0.00000 3 0.00000 0.18750 Objective Allowable Allowable Variable Coefficient Increase Decrease 1.00000 0.25000 0.10714 1.25000 0.15000 0.25000 RH3 Allowable Allowable Constraint Value Increase Decrease 4560.00000 1040.00000 560.00000 2400.00000 Infinite 560.00000 1600.00000 140.00000 297.14286 (a) What is the optimal solution, and what are the optimal production quantities? jars M jars profit $4 (b) Specify the objective function ranges. (Round your answers to five decimal places.) Western Foods Salsa 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 $0.188. O One additional ounce of whole tomatoes will improve profits by $560.00. O One additional ounce of whole tomatoes will improve profits by $0.125. O Additional ounces of whole tomatoes will not improve profits. constraint 2 O One additional ounce of tomato sauce will improve profits by $0.188. O One additional ounce of tomato sauce will improve profits by $560.0o. O One additional ounce of tomato sauce will improve profits by $0.125. O Additional ounces of tomato sauce vill not improve profits. constraint 3 O One additional ounce of tomato paste will improve profits by $0.188. O One additional ounce of tomato paste will improve profits by $560.0o. O One additional ounce of tomato paste will improve profits by $0.125. O Additional ounces of tomato paste vill 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
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