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?
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?
The correct options are
A x ≥ 0 and y ≥ 0
B 3x + 4y ≥ 8
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
A
x ≥ 0 and y ≥ 0
B
3x + 4y ≥ 8
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
