Linear programming examples, Operation Research

Solved LP Sample Assignment & Questions

A person desires to decide the ingredients of a diet which will satisfy his routine necessities of fats, proteins, and carbohydrates at the minimum cost. The selection is to be made from four different kinds of foods. The yields per unit of these foods are given below in the table.

Food Type

Yield/unit

Cost/Unit

Rs

Proteins

Fats

Carbohydrates

1

3

2

6

45

2

4

2

4

40

3

8

7

7

85

4

6

5

4

65

Minimum Requirement

800

200

700

 

Develop the LP for the problem.

Answer

Assume

x1 - number of units of food type l

     x2 - number of units of food type 2

     x3 - number of units of food type 3

     x4 - number of units of food type 4

 

Minimize Z = 45x1 + 40x2 + 85x3 + 65x4

Subject to

3x1 + 4x2 + 8x3 + 6x4 ≥ 800

2x1 + 2x2 + 7x3 + 5x4 ≥ 200

6x1 + 4x2 + 7x3 + 4x4 ≥ 700

                        x1≥0, x2 ≥0, x3≥0, x4≥0

 

Posted Date: 7/4/2012 3:18:32 AM | Location : United States







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