33 Clint Hanks has decided to try a new diet that promises enhanced muscle tone if the daily intake of five essential nutrients is tightly controlled. After extensive research, Clint has determined that the recommended daily requirements of these nutrients for a person of his age, height, weight, and activity level are as follows:

between 69 grams and 100 grams of protein, at least 700 milligrams of phosphorus, at least 420 milligrams of magnesium, between 1,000 milligrams and 1,750 milligrams of calcium, and at least 8 milligrams of iron. Given his limited finances, Clint has identified seven inexpensive food items that he can use to meet these requirements. The cost per serving for each food item and its contribution to each of the five nutrients are given in table 33.

(a) Use LP to identify the lowest cost combination of food items that Clint should use for his diet.

(b) Would you characterize your solution in

(a) as a well-balanced diet? Explain your answer.

FOOD ITEM (serving size)
PROTEIN (g)
PHOSPHORUS (mg)
MAGNESIUM (mg)
CALCIUM (mg)
IRON (mg)
COST PER SERVING ($)
Chicken Patty (0.25 pound) 17.82 250 29 23 1.14 0.50 Lasagna (300 grams) 24.53 223 56 303 2.52 0.58 2% Milk (1 cup) 8.05 224 27 293 0.05 0.42 Mixed Vegetables (1 cup) 5.21 93 40 46 1.49 0.24 Fruit Cocktail (1 cup) 1.01 26 11 15 0.62 0.37 Orange Juice (1 cup) 1.69 42 27 27 0.32 0.36 Oatmeal (1 packet) 4.19 136 46 142 10.55 0.18