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 275 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, 50.64, 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 st. oz of whole tomatoes 5W+7M 3W + 1M 2W + 2M s 4,400 $2,400 oz of tomato sauce s 1,600 oz of tomato paste W, M 20 The computersolution is shown below. Optinal objective value - 550.00000 Variable Value Reduced Cort W 600.00000 0.00000 M 200.00000 0.00000 enstraint Black/Burplus Dual Value 0.00000 0.12500 400.00000 0.00000 0.00000 0.19750 Objective Allowable Allowable Coefficient Increase Decrease 1.00000 0.25000 0.10714 1.25000 0.15000 0.25000 Allowable Allowable. Increase Decrease 4400.0000 1200.00000 400.00000 2400.00000 Infinite 400.00000 3 1600.00000 100.00000 342.85714 (a) What is the optimal solution, and what are the optimal production quantities? W jars M jars 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 One additional ounce of whole tomatoes will improve profits by $0.125. O One additional ounce of whole tomatoes will improve profits by $0.188. O One additional ounce of whole tomatoes will improve profits by $400.00. O Additional ounces of whole tomatoes will not improve profits. constraint 2 One additional ounce of tomato sauce will improve profits by $0.125. Variable W M Constraint 1 2 RHS Value (c) What are the dual values for each constraint? Interpret each. constraint 1 O One additional ounce of whole tomatoes will improve profits By $0.125. O One additional ounce of whole tomatoes will improve profits by $0.188. O One additional ounce of whole tomatoes will improve profits by $400.00. O Additional ounces of whole torkatoes 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 $0.188. One additional ounce of tomato sauce will improve profits by $400.00. O Additional ounces of tomato sauce will not improve profits. constraint 31 O One additional ounce of tomato paste will improve profits by $0.125. O One additional ounce of tomato paste will improve profits by $0.188. One additional ounce of tomato paste will improve profits by $400.00. 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 constraint 3 to to 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 275 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, 50.64, 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 st. oz of whole tomatoes 5W+7M 3W + 1M 2W + 2M s 4,400 $2,400 oz of tomato sauce s 1,600 oz of tomato paste W, M 20 The computersolution is shown below. Optinal objective value - 550.00000 Variable Value Reduced Cort W 600.00000 0.00000 M 200.00000 0.00000 enstraint Black/Burplus Dual Value 0.00000 0.12500 400.00000 0.00000 0.00000 0.19750 Objective Allowable Allowable Coefficient Increase Decrease 1.00000 0.25000 0.10714 1.25000 0.15000 0.25000 Allowable Allowable. Increase Decrease 4400.0000 1200.00000 400.00000 2400.00000 Infinite 400.00000 3 1600.00000 100.00000 342.85714 (a) What is the optimal solution, and what are the optimal production quantities? W jars M jars 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 One additional ounce of whole tomatoes will improve profits by $0.125. O One additional ounce of whole tomatoes will improve profits by $0.188. O One additional ounce of whole tomatoes will improve profits by $400.00. O Additional ounces of whole tomatoes will not improve profits. constraint 2 One additional ounce of tomato sauce will improve profits by $0.125. Variable W M Constraint 1 2 RHS Value (c) What are the dual values for each constraint? Interpret each. constraint 1 O One additional ounce of whole tomatoes will improve profits By $0.125. O One additional ounce of whole tomatoes will improve profits by $0.188. O One additional ounce of whole tomatoes will improve profits by $400.00. O Additional ounces of whole torkatoes 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 $0.188. One additional ounce of tomato sauce will improve profits by $400.00. O Additional ounces of tomato sauce will not improve profits. constraint 31 O One additional ounce of tomato paste will improve profits by $0.125. O One additional ounce of tomato paste will improve profits by $0.188. One additional ounce of tomato paste will improve profits by $400.00. 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 constraint 3 to to
