The Douglas family raises cattle on their firm in Virginia. They also have a large garden in which they grow ingredients for making two types of relish – chow-chow and top-tomato. These they sell in 16-ounce jars at local sores and craft fairs in the fall. The profit for a jar of chow-chow is $3.00 and the profit for a jar of top-tomato relish is $2.40. The main ingredients in each relish are cabbage, tomatoes and onions. A jar of chow-chow must contain at least 60% cabbage, 5% onions, and 10% tomatoes, and a jar of top-tomato relish must contain at least 50% tomatoes, 5% onions, and 10% cabbage. Both relishes contain no more than 10% onions. The family has enough time to make no more than 800 jars of relish. In checking sales records for the past five years they know that they will sell at least 30% more chow-chow than top-tomato relish. They will have 300 pounds of cabbage, 400 pounds of tomatoes, and 50 pounds of onions available. The Douglas family wants to know how many jars of each relish to produce to maximize profits.
a. Formulate a linear programming model for this problem
b. Solve the model using SOLVER