Tom’s, Inc., produces various Mexican food products and

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? If required, round your answers for W and M to the nearest whole number. If required, round your answer for Profit to the nearest dollar.

W
M
Profit	$

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 objective function will change by if you increase the constraint by one unit.

Whole tomatoes have a shadow price of .125 which means that if we add one ounce of whole tomatoes the value of the objective function would increase by $0.125 .

Tomato sauce has a shadow price of 0 which means that if we add one ounce of tomato sauce the value of the objective function would not change .

Tomato paste has a shadow price of .188 which means that if we add one ounce of tomato paste the value of the objective function would increase by $0.188 .

Constraints with a shadow price of 0 means that It is a non-binding constraint .

Identify each of the right-hand-side ranges. If required, round your answers to the nearest whole number. 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