Question

Solve the following linear programming problem graphically: 

Maximise Z = x + 2y

Subject to the constraints:

x − y ≥ 0

x − 2y ≥ −2 

x ≥ 0, y ≥ 0

Answer 1

Subject to constraints are

x − y ≥ 0 

x − 2y ≥ −2, 

x ≥ 0, y ≥ 0

Convert inequalities into equations, we get

x − y = 0     ...(i)

x − 2y = −2     ...(ii)

For x − y = 0

x	1	2
y	1	2

or x − 2y = −2

x	0	−2
y	1	0

The intersection point of the given equation is A(2, 2).

Corner point	Optimal value Z = x + 2y
O (0,0)	Z = 0
A (2, 2)	Z = 6

Since the feasible region is unbounded and the value of Z = x + 2y increases indefinitely, there is no finite maximum value of Z.