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 health 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 touse 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.

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

Work both parts a) and b). 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

1. Use linear programming to find the cost-minimalizing number of ounces of each ingredient that Nutmeg should use in each 4-ounce package. What is the percent package cost of raw materials?
2. 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, 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?

Answer rating: 100% (QA)

a Let x1 x2 and x3 be the ounces of Almond Walnut and Peanuts to be in... View the full answer