A dietician is planning the menu for the noon meal at an elementary school. He p

Question

A dietician is planning the menu for the noon meal at an elementary school. He plans to serve three main items, all having different nutritional content. The dietitian is interested in providing at least the minimum daily requirement of each of three vitamins in this one meal. The table below summarizes the vitamin content per ounce of each type of food, the cost per ounce, and minimum daily requirement for each vitamin. Any combination of the three foods may be selected as long as the total serving size is at least 6.0 ounces.

Formulate the linear programming problem that when solved would determine the number of ounces of each food to serve. The objective is to minimize the cost of the meal while satisfying minimum daily requirement levels of the three vitamins as well as the restriction on the minimum serving size.

**NOTE: Let A = # of oz. of Food A, B = # of oz. of Food B, and C = # of oz. of Food C.

SOLUTION:

Minimize z = _____ A + _____B + _____ C

Subject to:

(1) 20A + 40B + 30C ______

(2) _____ A +______ B +______ C   120

(3) ______ A _______+  B + ______ C ______

(4) A + B + C ________

(5) A,B,C _______

Vit 1 (mg) Vit 2 (mg) Vit 3 (mg) Cost per Ounce ($) Food A 20 10 20 0.15 Food B 40 25 30 0.18 Food C 30 15 25 0.22 MDR 240 120 180

Explanation / Answer

Minimize the cost of the meal

So, we gotta minimize
z = 0.15A + 0.18B + 0.22C ----> ANSWER

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Constraints :

20A + 40B + 30C talks about the vit3, which has gotta be 180
So, 20A + 40B + 30C >= 180 ---> ANSWER

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Now, vit2 :
10A + 25B + 15C >= 120 ---> ANSWER

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Now, vit 1 :
20A + 40B + 30C >= 240 ---> ANSWER

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Any combination of the three foods may be selected as long as the total serving size is at least 6.0 ounces.
So, we have
A + B + C >= 6 ----> ANSWER

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A , B , C >= 0 ---- >ANSWER

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