Question

Nutrient	Peanuts	Raisins	M&Ms	Mini-pretzels
Calories(kcal)	855	435	1024	162
Protein (g)	34.57	4.67	9.01	3.87
Fat (g)	72.50	0.67	43.95	1.49
Carbohydrates (g)	31.40	114.74	148.12	33.68

Suppose you want to make at most 10 cups of trail mix, using all of the ingredients. You dont want either ingredient to dominate the mixture so you want each ingredient to contribute at least 10% of the total volume of the mix made. You want the entire amount of trail mix to have no more than 7000 calories and you want to maximize the the amount of carbohydrates in the mix. (Use "solver" or an equivalent program because the simplex method gets to complicated)

1) What constraints must be placed on the objective function?

2) Find the number of cups of each ingredient in the mix so the amount of carbohydrates is maximized.

3) How many grams of carbohydrates are in a cup of the final mix? How many calories?

4) Under all the constraints given about, what recipe for the trail mix will maximize the amount of protein in the mix? How many grams of protein are in a cup of the mix? Calories?

5) Consider making a batch of trail mix under the following conditions: You still want to make at most 10 cups of trail mix, and you still want each of the ingredients to contribute at least 10% of the total volume of the mix made. You want the entire amount of trail mix you make to have at least 1000 grams of carboyhydrates, and you want to minimize the amount of fat in the mix. What recipe for trial mix will minimize the amount of fat in the mix?

6) How much fat, protein and carbohydrates are in a cup of this mix?

7) How many calories are in a cup of this mix?

Answer 1

Following are the trails prepared by gradual increase based on calculation in the each of the component.

Trail	Component 1	Component 2	Component 3	Component 4	Total Calories
1	855	435	1024	162	2476
2	940.5	478.5	1228.8	1782.2	2726
3	1026	565.5	1331.2	210.6	3133.4
4	1197	609	1638.4	226.8	3671.2
5	1282.5	739.5	1638.4	307.8	3968.2
6	1282.5	957	1638.4	356.4	4234.3
7	1368	1087.5	1740.8	421.2	4617.5
8	1368	1218	1740.8	453.6	4780.4
9	1410.7	1305	1740.8	486	4942.5
10	1581.7	1392	1740.8	502.2	5216.7

1. Main Constarins are: it is difficult to maintain calories verses fat. Balancing of these two difficult.

2. There is gagradual increase in Carbohydrate in all the cups.

3. 4682.1 grams of Carbohydrate is present.

4. 10th trail posses maximum amount of Protein.

5. 10th trail contain minimum amount of Fat.

6. 555.07 grams of Protein is present.

7. 5216.7 Calories are present in this cup.