Mr. Chris Zhang is the food and beverage manager for XTreme Fit. His company is fielding a team to compete at this years' Fitness Olympics. Xtreme Fit decided to put their team on a diet to prepare them for the competition. Mr. Zhang was tasked to determine the menu for the team. The head coach of the team set the following nutritional guidelines for each meal: At least 5 mg of iron
At least 30 g of protein
At least 40 g of carbohydrates
At least 20 but no more than 60 g of fat
No more than 30 mg of cholesterol
Between 1,500 and 2,000 calories
Mr. Zhang prepares the meals from a few basic food groups. These items are listed below with the nutritional content per pound. The cost of the item per pound are as follows:
Red meat: $2.30
White meat: $0.80
Seafood: $3.70
Legumes: $0.90
Leafy greens: $0.75
Starch: $0.40
Dairy: $0.83
The nutritional content of each food group are as follows:
Iron (mg/lb.) Protein (g/lb.) Carbohydrates (g/lb.) Fat (g/lb.) Cholesterol (mg/lb.) Calories (per lb.)
Red meat 0.3 82 0 75 350 860
White meat 4.4 17 0 30 180 520
Seafood 3.3 85 0 5 90 500
Legumes 3.4 10 30 3 0 600
Leafy greens 0.5 6 0 0 0 50
Dairy 0.2 16 22 10 20 240
Starch 2.2 10 70 0 0 460
Instructions:
Part 1:
1) Determine the optimum solution for this problem.
2) Formulate and show your complete linear programming model for this problem. Type your final answer in the space provided for this problem.
Part 2: Answer these questions:
2.1) If a serving of each of the food items (other than dairy) was limited to no more than half a pound, what effect would this have on your optimal solution?
2.2) Recommend a strategy for XTreme Fit.