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