36.Healthtech Food Products is considering developing a new low-fat snack food. It is to be a blend of two types of cereals, each of which has different fiber, fat, and protein characteristics. The following table shows these nutrition characteristics for one ounce of each type of cereal.
CerealDietary Fiber (grams)Fat (grams)Protein (grams)
A224
B1.533
Note that each ounce of cereal A provides 2 grams of dietary fiber and that each ounce of cereal B provides 1.5 grams of dietary fiber. Thus, if Healthtech were to develop the new product using a mix consisting of 50% of cereal A and 50% cereal B, 1 ounce of the snack food would contain 1.75 grams of dietary fiber. Healthtech’s nutrition requirements call for each ounce of the new food to have at least 1.7 grams of dietary fiber, no more than 2.8 grams of fat, and no more than 3.6 grams of protein. The cost of cereal A is $0.02 per ounce and the cost of cereal B is $0.025 per ounce. Healthtech wants to determine how much of each cereal is needed to produce 1 ounce of the new food product at the lowest possible cost.
a.Formulate a linear programming model for this situation.
b.Solve the problem using the graphical solution procedure.
c.What are the values of the slack and surplus variables?
d.If Healthtech markets the new snack food in an 8-ounce package, what is the cost per package?
47.Reconsider the Kelson Sporting Equipment, Inc., production example in Problem 22. Discuss the concepts of infeasibility, unbounded solutions, and alternative optimal solutions as they occur in each of the following situations:
a.Management requested that the production of baseball gloves (regular model plus catcher’s model) be such that the total number of gloves produced is at least 750.
b.The original problem must be solved again because the profit contribution for the regular model is adjusted downward to $4 per glove.
c.What would have to happen for this problem to be unbounded?