Question

The feasible solutions for a linear programming problem with constraints
x ≥0, y ≥ 0
3x+5y ≤ 15
5x+2y ≤ 10
is equal to

• A. $(1,-1),(0,0)$
• B. $(-3,5),(1,-1)$
• C. $(0,0),(-3,5)$
• D. $(2,0),(0,0)$

Answer 1

The correct option is D $(2,0),(0,0)$

In the last session we saw feasible region formed by the constraints of a linear programming problem. Feasible solution is any point in the feasible region.

We can also say a feasible solution is the values of decision variables( x and y) which satisfy the constraints given to us.

We will go through each option and see which among them satisfy our conditions x ≥ 0,y ≥ 0

3x+5y ≤ 15, 5x+2y ≤ 10.

The points (1,-1) and (-3, 5) clearly does not satisfy the constraints because we want both the coordinates to be non negative as x ≥ 0, y ≥ 0 are two constraints.

(0,0) and (2,0) satisfy all the conditions given.