Suppose that there are six foods and their detail are as follows: Food Serving S

Question

Suppose that there are six foods and their detail are as follows:




Food


Serving Size


Energy

(kcal)


Protein

(g)


Calcuim

(mg)


Price

(rupees/serving)


Limit

(servings/day)

Oatmeal
28g
110
4
2
3
4



Chicken
100g
205
32
12
24
3

Eggs
2 Large
160
13
54
13
2

Whole Milk
237cc
160
8
285
9
8

Cherry Pie
170g
420
4
22
20
2

Pork & Beans
260g
260
14
80
19
2




After consulting with nutritionists, we decree that a satisfactory diet has at least 2000 kcal of energy, 55 g of protein, and 800 mg of calcium (vitamins and iron are supplied by pills). While some of us would be happy to subsist on 10 servings of pork and beans, we have decided to impose variety by having a limit on the number of servings/day for each of our six foods. What is the least cost of satisfactory diet? Construct an LP model of this problem.

Explanation / Answer

#: amount x1: # of oatmeal x2: # of chicken x3:# of egg x4:# of whole milk x5:# of cherry pie x6:# of pork & beans 110x1 + 205x2 + 160x3 + 160x4 + 420x5 + 260x6 => 2000 4x1 + 32x2 + 13x3 + 8x4 + 4x5 + 14x6 => 55 2x1 + 12x2 + 54x3 + 285x4 + 22x5 + 80x6 =>800 x1,x2,x3,x4,x4...

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