solved lp sample assignment amp questionsa person

Question

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