Toms produces various food products and sels them to Western Food. a chain of gr
ID: 353172 • Letter: T
Question
Toms produces various food products and sels them to Western Food. a chain of grocery stores located in Texas and New Mexico. Tom's makes two sales 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, 20% tomato sauce, tomato paste. Each jar of Salsa produced weighs 10 ounces. For the current production period, Toms Inc can purchase 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 other spices and the other ingredients is approximately $0.10 per jar. Toms 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 Inc contract results in sales revenue of $0.64 for each jar of Western Foods Salsa and $1.93 for each jar of Mexico City Salsa. Develop a linear programming model that will enable Toms to determine the mix of sales products that will maximize the total profit contribution.Explanation / Answer
Product Price ($) WT (oz.) TS (oz.) TP (oz.)
Western Foods Salsa 0.64 5 3 2
Mexico City Salsa 1.93 7 2 1
Capacity 4480 2080 1600
Cost $0.06 $0.04 $0.035
WT: Whole tomatoes,
TS: Tomato sauce,
TP: Tomato paste
Cost of product per jar = ingredients + jar + WT + TS + TP
Cost of Western Foods Salsa per jar = 0.10+0.03+0.3+0.12+0.07 = $0.62
Cost o f Mexico City Salsa per jar = 0.10+0.03+0.42+0.04+0.07 = $0.66
Decision variables;
x1 Amount of Western Foods Salsa produced
x2 Amount of Mexico City Salsa produced
Profit function; Profit = Income – Cost
Z = (0.64x1 + 1.93x2) (0.62x1 + 0.66x2)
Z = 0.02x1 + 1.27x2
LP Model;
Maximize Z = 1.02x1 + 1.27x2
Subject to:
5x1 + 7x2 4480 WT
3x1 + x2 2080 TS
2x1 + 2x2 1600 TP
x1, x2 0