A problem often of concern to managers in processing industries is blending. The Nutmeg Corporation, from Problem 15, is considering a new product it intends to sell to active and health-concerned adults. This new product will be a 4-ounce package of nuts that conforms to specific heath requirements. First, the 4-ounce package can contain no more than 720 calories. It must deliver at least 20 grams of protein. Finally, the package must provide at least 15 percent of the adult daily requirement (ADR) of calcium and 20 percent of the ADR of iron. Nutmeg would like to use only almonds, walnuts, and peanuts in this new product. The following table provides nutritional data on each of these ingredients as well as their cost to Nutmeg.

a. Use linear programming to find the cost-minimizing number of ounces of each ingredient that Nutmeg should use in each 4-ounce package. What is the per package cost of raw materials?
b. The marketing department at Nutmeg insists that each package should contain at least 0.5 ounce of almonds, at least 0.5 ounce of walnuts, and no more than 1 ounce of peanuts. Does the solution developed for part (a) satisfy these new constraints? If not, use linear programming to find a solution that includes these marketing requirements. What is the new cost of raw materials?

Data from problem 15

The Nutmeg Corporation produces three different products, each in a 1-pound can: Almond-Lovers Mix, Walnut-Lovers Mix, and the Thrifty Mix. Three types of nuts are used in Nutmeg's products: almonds, walnuts, and peanuts. Nutmeg currently has 350 pounds of almonds, 150 pounds of walnuts, and 1,000 pounds of peanuts. Each of Nutmeg's products must contain a certain percentage of each type of nut, as shown in the following table. The table also shows the revenue per can as well as the cost per pound to purchase nuts.

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Calories Grams of Protein per Ounce 6 4 7 per Ounce Ingredients Almonds 180 Walnuts 190 Peanuts 170 Percent ADR of Calcium per Ounce 8% 2% 0% Percent ADR of Iron per Ounce 6% 6% 4% Cost per Ounce $0.28 $0.38 $0.12