Question

Reshma wishes to mix two types of food P and Q in such a way that the vitamin contents of the mixture contain at least 8 units of vitamin A and 11 units of vitamin B. Food P costs Rs 60/kg and Food Q costs Rs 80/kg. Food P contains 3 units /kg of vitamin A and 5 units/kg of vitamin B while food Q contains 4 units /kg of vitamin A and 2 units /kg of vitamin B.Let the mixture contain x kg of food P and y kg of food Q. Which of the following are the constraints of this linear programming problem?

• A. x ≥ 0 and y ≥ 0
• B. 3x + 4y ≥ 8
• C. 5x + 2y ≥ 11
• D. x+y < 20

Answer 1

Answer: (A), (B), (C)

5x + 2y ≥ 11

The given information can be compiled in a table as follows.

The mixture must contain at least 8 units of vitamin A and 11 units of vitamin B.

We are given that the mixture contains x kg of food P and y kg of food Q

Therefore,

3x + 4y ≥ 8

5x + 2y ≥ 11

Since x and y are quantities, we have x ≥ 0 and y ≥ 0.

These inequalities or equations or restrictions on the variables of a linear programming problem are called constraints. In this particular problem, we have three constraints,

3x + 4y ≥ 8

5x + 2y ≥ 11

x ≥ 0 and y ≥ 0