QUESTION 2

Angela and Bob Ray keep a large garden in which they grow cabbage, tomatoes, and onions to make two kinds of relishchow-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 relish 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. Solve this model graphically.

a) Are there any resources left over and not used at the optimal solution point? Explain (10 marks)

b) The Rays have checked their sales records for the past 5 years and have found that they sell at least 50% more chow-chow than tomato relish. How will this additional information affect their model and solution? (10 marks)

c) Is there any alternate optimal solutions? Explain why or why not (5 marks