Matthew Williams
Craig Hildebrand
Math 131 (MoWe 10:45-12)
December 10, 2014

Chapter 3 Project
Balancing Nutrients

In preparing a recipe, you must decide what ingredients and how much of each ingredient you will use. In these health-conscious days, you may also want to consider the amount of certain nutrients in your recipe. You may even be interested in minimizing some quantities (like calories or fat) or maximizing others (like carbohydrates or protein). Linear programming techniques can help to do this.
For example, consider making a very simple trail mix from dry-roasted, unsalted peanuts and seedless raisins. Table 1 lists the amounts of various dietary quantities for these ingredients. The amounts are given per serving of the ingredient. Nutrient | Peanuts ServingSize = 1 Cup | Raisins ServingSize = 1 Cup | Calories (kcal) | 850 | 440 | Protein (g) | 34.57 | 4.67 | Fat (g) | 72.50 | 0.67 | Carbohydrates (g) | 31.40 | 114.74 |

Suppose that you want to make at most 6 cups of trail mix for a day hike. You don’t want either ingredient to dominate the mixture, so you want the amount of raisins to be at least ½ of peanuts and the amount of peanuts to be at least ½ of the amount of raisins. You want the entire amount of trail mix you make to have fewer than 4000 calories, and you want to maximize the amount of carbohydrates in the mix. 1. Let x be the number of cups of peanuts you will use, let y be the number of cups of raisins you will use, and let c be the amount of carbohydrates in the mix. Find the objective function.
31.4x+114.74y=c

2. What constraints must be placed on the objective function?

* x must be at least half of y. Denoted as y≥12x * y must be at least half of x. Denoted as x≥12y * Sum of x and y must not be greater than 6 cups. Denoted as x+y≤6 * Total amount must have less than 4,000 calories.