Question

Healthy Snacks Co. produces snack mixes. Recently, the company has decided to introduce a new snack mix that has peanuts, raisins, pretzels, dries cranberries, sunflower seeds and pistachios. Each bag of the new snack is designed in order to hold 250 grams of the snack. The company has decided to market the new product with a emphasis on its health benefits. After consulting nutritionists, Healthy Snacks decides to mix the ingredients so that the snack has the following specifications:

1 - Total calories <= 800  

2 - Fat <= 20

3 - Sodium <= 200

4 - Potassium <= 700

5 - Carb <= 140

6 - Protein >= 10

7 - Vitamin A >= 3

8 - Vitamin B6 >= 25

9 - Vitamin C >= 2

10 - Iron >= 15

11 - Calcium >= 5

Table below shows the amount of each nutrition in each snack's ingredient per 1 gram:

	peanut	raisin	pretzel	dried cranberries	sunflower seed	pistachio
Calories	5.67	3.00	1.00	3.08	5.84	5.62
Fat (g)	0.49	0.00	0.01	0.01	0.51	0.06
Sodium (mg)	0.18	0.12	3.32	0.03	0.09	0.01
Potassium (mg)	7.05	7.49	0.36	0.40	6.45	10.25
Carb (g)	0.16	0.79	0.21	0.83	0.20	0.28
Protein (g)	0.26	0.03	0.03	0.00	0.21	0.20
Vitamin A (%)	0.00	0.00	0.00	0.00	0.01	0.08
Vitamin B-6 (%)	0.17	0.12	0.00	0.00	0.68	0.85
Vitamin C (%)	0.00	0.02	0.00	0.00	0.02	0.09
Iron (%)	0.25	0.09	0.07	0.03	0.29	0.21
Calcium (%)	0.09	0.05	0.00	0.00	0.07	0.10

Table below shows the cost of each ingredients per 1 gram:

	peanut	raisin	pretzel	dried cranberries	sunflower seed	pistachio
cost per 1 gram ($)	$ 0.005	$ 0.020	$ 0.013	$                     0.013	$                  0.022	$     0.031

Per marketing department research, each bag of snack should have at least 10 grams of each ingredient. Having this information, answer the following questions. Please make sure that the information is easy to read and understand.

1. Formulate a LP for Healthy Snacks to minimize total cost of producing one bag of snack while satisfying all constraints. Clearly state your decision variables, objective function and constraints. USING EXCEL WORKSHEET.

Answer 1