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 280 pounds of whole tomatoes, 130 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 following formulation:
Max 1W + 1.25M
s. t.
5W + 7M ? 4480 Whole tomatoes
3W + 1M ? 2080 Tomato sauce
2W + 2M ? 1600 Tomato paste
W, M ? 0
The sensitivity report is shown in figure below.
Optimal Objective Value = 860.00000
Variable Value Reduced Cost
W 560.00000 0.00000
M 240.00000 0.00000
Constraint Slack/Surplus Dual Value
1 0.00000 0.12500
2 160.00000 0.00000
3 0.00000 0.18750
Variable Objective
Coefficient
Allowable
Increase
Allowable
Decrease
W 1.00000 0.25000 0.10714
M 1.25000 0.15000 0.25000
Constraint RHS
Value
Allowable
Increase
Allowable
Decrease
1 4480.00000 1120.00000 160.00000
2 2080.00000 Infinite 160.00000
3 1600.00000 40.00000 320.00000
What is the optimal solution, and what are the optimal production quantities?
Specify the objective coefficient ranges. Round your answers to three decimal places. If there is no lower or upper limit, then enter the text "NA" as your answer.
Variable Objective Coefficient Range
lower limit Upper limit
Western Foods Salsa
Mexico City Salsa
What are the shadow prices for each constraint? Round your answers to three decimal places.
Constraint Shadow Price
Whole tomatoes
Tomato sauce
Tomato paste
Interpret each shadow price.
The shadow price is the value that the will change by if you increase the constraint by one unit.
Whole tomatoes have a shadow price of which means that if we add one pound of whole tomatoes the value of the objective function would .
Tomato sauce has a shadow price of which means that if we add one pound of tomato sauce the value of the objective function would .
Tomato paste has a shadow price of which means that if we add one pound of tomato paste the value of the objective function would .
Constraints with a shadow price of 0 means that .
Identify each of the right-hand-side ranges. If there is no lower or upper limit, then enter the text "NA" as your answer.
Constraint Right-Hand-Side Range
lower limit upper limit
Whole tomatoes
Tomato sauce
Tomato paste