Tom’s, Inc., produces various Mexican food products and sells them to Western Foods, a

Question: 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
Show transcribed image text 100% (1 rating)a) W = 520 M = 280 Profit = 1W 1.25M =1*520 1.25*280 =870 b) Western Foods salsa : objective coefficient-allowable decrease = 1-0.10714 = 0.89286 to objective coefficient allowable incr…View the full answerTranscribed 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% 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, 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 ≤ 4,560 oz of whole tomatoes 3W 1M ≤ 2,240 oz of tomato sauce 2W 2M ≤ 1,600 oz of tomato paste W, M 20 The computer solution is shown below. Optimal Objective Value 870.00000 Value Reduced Cost 520.00000 280.00000 0.00000 0.00000 M Dual Value Constraint 1 0.12500 0.00000 3 0.18750 Variable Objective Coefficient Allowable Allowable Increase Decrease 1.00000 0.25000 0.10714 M 1.25000 0.15000 0.25000 Constraint Allowable Allowable Value Increase Decrease 4560.00000 1040.00000 400.00000 2240.00000 1600.00000 Infinite 100.00000 400.00000 297.14286 (a) What is the optimal solution, and what are the optimal production quantities? W jars jars M profit $ (b) Specify the objective function ranges. (Round your answers to five decimal places.) Western Foods Salsa to to Mexico City Salsa (c) What are the dual values for each constraint? Interpret each. constraint 1 O One additional ounce whole tomatoes will improve profits by $0.125. O One additional ounce whole tomatoes will improve profits by $400.00. One additional ounce of whole tomatoes will improve profits by $0.188. Additional ounces 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 $400.00. O One additional ounce of tomato sauce will improve profits by $0.188. 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 $400.00. O One additional ounce of tomato paste will improve profits by $0.188. 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 slack/Surplus 0.00000 400.00000 0.00000