A mountain climber planning an epedition is concerned about two types of synthetic food.
One food contains 100 calories per ounce, 24 units of protein per ounce, and 4 units of fat per ounce. A second food contain 125 calories per ounce, 20 units of protein per ounce, and10 units of fat per ounce.
If the man wants a minimum of 2,000 calories, 400 units of protein, and 100 units of fat per day, which food or food combination should he use to meet the minimum daily requirements and minimize the total wight?
Use two variables and translate the constraints to a system of linear inequalities. Graph the system, and find the vertices, apply linear programming theory and interpret the results.