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.

1. (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?

2. (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?

For part b), if the solution in part a) does not satisfy the marketing requirements, just provide the additional constraints that are required for the marketing requirements to be satisfied. You do not need to resolve the linear programming problem

Ingredients Calories Grams of Percent ADR of Percent ADR of Cost per Protein per Calcium per Iron per Ounce per Ounce Ounce Ounce Ounce $0,28 Almonds 180 6% 6 8% Walnuts $0,38 190 4 2% 6% $0,12 Peanuts 170 4% 7 0%