Section 3.4 A dietician at People\'s Hospital is charged with designing a good d

Question

Section 3.4 A dietician at People's Hospital is charged with designing a good diet for patients who are diabetic. She determines that all the food she will include in a dinner meal will include vegetables, meat, cheese, and fruits. The following four foods are available today for this diet: cauliflower, veal, Jarlsberg cheese, and apples. Each serving portion of cauliflower costs 62C, each small portion of veal costs $2.97, each slice of Jarlsberg Cheese costs 58c, and each apple costs 79c. Each patients must ingest at a dinner at least 600 calories, 25 oz. of glucose, 120 oz. of protein and 85 oz. of fiber. The nutritional content per serving per unit of each food is shown in the table below. Formulate a linear program that can be used to satisfy the nutritional requirements that the dietician has set for her diabetic patients at a minimal cost. Type of Food Cauliflower Fiber ounces) 15 10 10 20 Glucose ounces) Calories (per serving) 20 85 100 Protein ounces) 10 65 Veal 0 Jarlsberg Cheese Apple 12 25

Explanation / Answer

let x1 be the price per unit serving calories

let x2 be the price per unit Glucose ounces

let x3 be the price per unit Protine ounces

let x4 be the price per unit Fiber ounces

this implies,

min Z=600x1+25x2+120x3+85x4

Subject to constraint

20 x1 + 2 x2 + 10 x3 + 15 x4 <= 62

85 x1 + 0 x2 + 65 x3 + 10 x4 <= 2.97

100 x1 + 3 x2 + 55 x3 + 10 x4 <= 58

55 x1 + 12 x2 + 25 x3 + 20 x4 <= 79

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