[solved]-Problem 3 09 Tom S Inc Produces Various Mexican Food Products Sells Western Foods Chain Gr Q39669241

Problem 3-09

Tom’s, Inc., produces various Mexican food products and sellsthem to Western Foods, a chain of grocery stores located in Texasand New Mexico. Tom’s, Inc., makes two salsa products: WesternFoods Salsa and Mexico City Salsa. Essentially, the two productshave different blends of whole tomatoes, tomato sauce, and tomatopaste. 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% wholetomatoes, 10% tomato sauce, and 20% tomato paste. Each jar of salsaproduced weighs 10 ounces. For the current production period,Tom’s, Inc., can purchase up to 280 pounds of whole tomatoes, 130pounds of tomato sauce, and 100 pounds of tomato paste; the priceper pound for these ingredients is $0.96, $0.64, and $0.56,respectively. The cost of the spices and the other ingredients isapproximately $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 WesternFoods results in sales revenue of $1.64 for each jar of WesternFoods Salsa and $1.93 for each jar of Mexico City Salsa.

LettingW = jars of Western Foods SalsaM = jars of Mexico City Salsaleads to the following formulation:Max1W+1.25Ms.t.5W+7M≤4480  Whole tomatoes3W+1M≤2080  Tomato sauce2W+2M≤1600  Tomato pasteW, M ≥ 0

The sensitivity report is shown in figure below.

Optimal Objective Value=      860.00000VariableValueReduced CostW560.000000.00000M240.000000.00000ConstraintSlack/SurplusDual Value10.000000.125002160.000000.0000030.000000.18750VariableObjective
CoefficientAllowable
IncreaseAllowable
DecreaseW1.000000.250000.10714M1.250000.150000.25000ConstraintRHS
ValueAllowable
IncreaseAllowable
Decrease14480.000001120.00000160.0000022080.00000Infinite160.0000031600.0000040.00000320.00000

1. What is the optimal solution, and what are the optimalproduction quantities? If required, round your answers for W and Mto the nearest whole number. If required, round your answer forProfit to the nearest dollar.
   WMProfit$  
2. Specify the objective coefficient ranges. Round your answers tothree decimal places. If there is no lower or upper limit, thenenter the text “NA” as your answer.
   VariableObjective Coefficient Rangelower limitUpper limitWestern Foods SalsaMexico City Salsa
3. What are the shadow prices for each constraint? Round youranswers to three decimal places. If your answer is zero enter”0″.
   ConstraintShadow PriceWhole tomatoesTomato sauceTomato paste
   Interpret each shadow price.

   The shadow price is the value that the objectivefunction  will change by if you increase the constraintby one unit.

   Whole tomatoes have a shadow price of 0.125  which meansthat if we add one ounce of whole tomatoes the value of theobjective function would increase by $0.125 .

   Tomato sauce has a shadow price of 0  which means that ifwe add one ounce of tomato sauce the value of the objectivefunction wouldnot change .

   Tomato paste has a shadow price of 0.188  which meansthat if we add one ounce of tomato paste the value of the objectivefunction would increase by $0.188 .

   Constraints with a shadow price of 0 means that it is a non-bindingconstraint .

4. Identify each of the right-hand-side ranges. If required, roundyour answers to the nearest whole number. If there is no lower orupper limit, then enter the text “NA” as your answer.
   ConstraintRight-Hand-Side Rangelower limitupper limitWhole tomatoesTomato sauceTomato paste

Expert Answer

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Answer to Problem 3-09 Tom’s, Inc., produces various Mexican food products and sells them to Western Foods, a chain of grocery sto… . . .