Case Study: Angela and Bob Ray keep a large garden in which they grow cabbage, tomatoes, and onions to make two kinds of relish-chow-chow and tomato. The chow-chow is made primarily of cabbage, whereas the tomato relish has more tomatoes than does the chow-chow. Both relishes include onions, and negligible amounts of bell peppers and spices. A jar of chow-chow contains 8 ounces of cabbage, 3 ounces of tomatoes, and 3 ounces of onions, whereas a jar of tomato rel- ish contains 6 ounces of tomatoes, 6 ounces of cabbage, and 2 ounces of onions. The Rays grow 120 pounds of cabbage, 90 pounds of tomatoes, and 45 pounds of onions each summer. The Rays can produce no more than 24 dozen jars of relish. They make $2.25 in profit from a jar of chow- chow and $1.95 in profit from a jar of tomato relish. The Rays want to know how many jars of each kind of relish to produce to generate the most profit.

a. Formulate a linear programming model for this problem.

b. Give a brief summary of the problem.

c. The main challenges faced on this project included a limitation on Labor and so fourth. Thanks, that is a good question. It doesn't have to be about labor, it just what is the challenges that Angela and Bob may run into while starting/doing this project.

d. Could the company increase its profit by increasing or decreasing?