Tom's Inc., produces various Mexican food products and sells them to Whole Foods, a chain of grocery stores located in the United States. Tom's Inc. makes two salsa products: Whole Foods Salsa and Mexico City Salsa. The two products have different blends of whole tomatoes, tomato sauce, and tomato paste. The Whole 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, is comprised 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 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 Whole Foods results in sales revenue of $1.64 for each jar of Whole Foods Salsa and $1.93 for each jar of Mexico City salsa.
a. Develop a linear programming model that will enable Tom's Inc. to determine the mix of salsa products that will maximize the total profit contribution.
b. Find the optimal solution.
Note: Units for constraints should be in ounces
Let W = # of jars of Whole Foods Salsa produced
Let M = # of jars of Mexico City Salsa produced
Show all work involving conversions and costs of the two products.