Geometrical Solution Of
Linear Programming Problem
Question: Find a geometrical interpretation and solution of the following LP problem:
Maximize z = 3x₁ + 5x₂
subject to restrictions
x₁ + 2x₂ ≤ 2000 (time restraint)
x₁ + x₂ ≤ 1500 (plastic restraint)
x₂ ≤ 600 (dress restraint)
and x₁ ≥ 0, x₂ ≥ 0 (non-negative restrictions)
Here is the graphical solution,
① Graph inequality constraints
Consider two mutually perpendicular lines Ox₁ and Ox₂. Any point in the positive quadrant satisfies non-negative restrictions i.e. x₁ ≥ 0, x₂ ≥ 0
Plot a line representing x₁ + 2x₂ = 2000
Clearly any point below line x₁ + 2x₂ = 2000 satisfies x₁ + 2x₂ ≤ 2000. This region is coloured blue here.
Similarly plot other lines to represent x₁ + x₂ ≤ 1500 and x₂ ≤ 600
② Find the feasible region or solution space.
As shown in figure any point in the shaded area is a feasible solution to the given LPP.