1. Perfect Weight Corporation (PW) operates several weight loss clinics in several cities in the eastern part of our country. It produces a wide variety of meals for consumption by its clients. The meals are monitored for their nutritional content to ensure that the clients are eating a healthy balanced diet. One such meal consists of food items that would be some combination of non-vegetarian items, vegetation items, grain items, and liquid items. They want to determine the quantity of each item to include in the meal with an objective to minimize the cost of the meal while satisfying the nutritional requirements.

The following table lists information about the food items and their nutritional makeup.

List of restrictions:

Nutritional requirements

1. Must have at least 450 calories
2. Must have at most 550 calories
3. Calories from fat must not exceed 35% of the actual total calories present in the meal
4. Must have at least 440 mg of nutrition item 1
5. Must have at least 10 mg of nutrition item 2
6. Must have at least 48,000 mg of nutrition item 3

Taste and practical requirements

7. Non-vegetarian item A (NVA) must be at least 60 grams
8. Non-vegetarian Item B (NVB) must account for at least 50% of the weight of NVA in the meal
9. Non-vegetarian Item B (NVB) must account for at most 75% of the weight of NVA in the meal
10. Grain Item A (GA) must be at least 30 grams in weight
11. Must include at least 80 grams of vegetation items (VGA or VGB or a combination of the two)
12. Must have at least cup of Liquid item A
13. Must have at least cup of Liquid item B
14. Must not have more than 1 cups of liquid items (LA or LB or a combination)

1. Formulate the problem as a linear program with an objective to minimize the cost and subject to various restrictions given above.

a) Write the algebraic formulation.

2. Show the image of the optimal solution of the Solver output below

3. What is the cost of the meal to the nearest dollar and cents?

What are the quantities of the items included in the meal?

Item Serving Total Calories Calories from fat Nutrition 1 Nutrition 2 Nutrition 3 Cost Food Details Code Size per serving per serving (mg/serving) (mg/serving) (mg/serving) ($/serving) Non Vegetarian Item A NVA 100 gm 191 61 30000 $3.20 Non Vegetarian Item B NVB 100 gm 70 45 5 $1.90 Vegetarian Item A VA 100 gm 55 40 56 8000 $1.20 Vegetarian Item B VB 100 gm 25 620 6000 $0.90 Grain Item A GA 120 31 2000 $0.65 Liquid Item A LA 1 cup 90 85 8000 $0.70 Liquid Item B LB 111 $1.00 4 100 gm 1 cup 330 60 Item Serving Total Calories Calories from fat Nutrition 1 Nutrition 2 Nutrition 3 Cost Food Details Code Size per serving per serving (mg/serving) (mg/serving) (mg/serving) ($/serving) Non Vegetarian Item A NVA 100 gm 191 61 30000 $3.20 Non Vegetarian Item B NVB 100 gm 70 45 5 $1.90 Vegetarian Item A VA 100 gm 55 40 56 8000 $1.20 Vegetarian Item B VB 100 gm 25 620 6000 $0.90 Grain Item A GA 120 31 2000 $0.65 Liquid Item A LA 1 cup 90 85 8000 $0.70 Liquid Item B LB 111 $1.00 4 100 gm 1 cup 330 60