HIGH PROTEIN/LOW CARBOHYDRATE DIET. One of the current diets that seems to produce substantial weight loss...

HIGH PROTEIN/LOW CARBOHYDRATE DIET. One of the current diets that seems to produce substantial weight loss in some persons is the high protein/low carbohydrate diet advocated by such authors as Atkins in his book, Diet Revolution, and Eades and Eades in their book, Protein Power. Although many nutritionists are concerned about the side effects of these diets, others feel the potential risks are outweighed (no pun intended) by the weight loss.

The following table gives the grams of fat, carbohydrates, and protein as well as the calorie count in four potential foods: steak (8 oz. portion), cheese (1 oz.), apples (1 medium), and whole milk (8 oz.). Jim Blount, a 45-year-old male, has done the calculations suggested in these books and has determined that he should have a calorie intake of between 1800 and 2000 calories and protein intake of at least 100 grams, but he should not consume more than 45 grams of carbohydrates daily. For breakfast Jim had two eggs and three strips of bacon, one piece of buttered high protein toast, and water. This breakfast contained 390 calories, 15 grams of carbohydrates, 20 grams of protein, and 29 grams of fat. Although these diets do not limit fat intake, Jim wishes to minimize his total fat consumed by constructing a diet for lunch and dinner consisting of only the four foods listed in the table. What do you recommend?

	Calories	Fat (grams)	Protein (grams)	Carbohydrates (grams)
Steak (8 oz. portion)	692	51	57	0
Cheese (1 oz.)	110	9	6	1
Apple (1 medium)	81	1	1	22
Milk (8 oz.)	150	8	8	12

Expert Solution

Optimal diet composition is determined using Linear Programming model as below

Formula:

B6 =SUMPRODUCT(B2:B5,$F$2:$F$5) copy to B6:E6

B8 =SUM(B6:B7) copy to B8:E8

Optimal solution:

Steak (8 oz. portion) = 1.5

Cheese (1 oz.) = 0

Apple (1 medium) = 0

Milk (8 oz.) = 2.5

keosha answered 1 year ago

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