Comprehensive Guide to Linear Programming in Decision Making

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The solution of this linear programming equation can be obtained through simplex method or graphical method. If we graph the constraints, we obtain the graph below with the shaded region representing a feasible solution. The corner coordinates give the solution to the equations. However, to determine the optimal solution, we substitute the corner coordinates in the objective function.

The corners solutions to problem include

B. x1=0, x2=2

C. x1=5/3 x2 =2/3

D.  x1=0, x2= 1.5

We apply the coordinates of the corner solution to the objective function to obtain optima solution

B. (x1=2, x2=0) = 2+0*0.5 = 2

C. (x1=1.5 x2=1) = 5/3 + 2/3*0.5 = 2

D. (x1=0 x2= 1.5) = 0 +1.5*0.5 = 3/4

The objective is to maximize x1+ 0.5x2 and in this case the objective function is maximized at (x1=2, x2=0; x1=5/3, x2=2/3). Therefore, the solution x1=5/3, x2, =2/3 is optimum. However, solution A(x1=0, x2=4) is not feasible as shown in the graph above. The solution is therefore not optimum. The same would apply to solution E(x1=3, x2=0) because it is not feasible and therefore not optimum.

September 25, 2023

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