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
x_{1 } number of units of food type l
x_{2 } number of units of food type 2
x_{3 } number of units of food type 3
x_{4 } number of units of food type 4
Minimize Z = 45x_{1} + 40x_{2} + 85x_{3 }+ 65x_{4}
Subject to
3x_{1} + 4x_{2} + 8x_{3} + 6x_{4 }≥ 800
2x_{1} + 2x_{2} + 7x_{3} + 5x_{4 }≥ 200
6x_{1} + 4x_{2} + 7x_{3} + 4x_{4 }≥ 700
x_{1}≥0, x_{2} ≥0, x_{3}≥0, x_{4}≥0