Tutorial Exercise on LP Solution Using DecisionPro Software

Transfer the following LP formulation to the DecisionPro software:

Max Z= 40X1+30X2
s.t.

2X1+2X2<=40
4X1+3X2<= 120
X1, X2>=0

The DecisionPro software steps:

Step 1.Type the objective function on the text bar in which curser is waiting for you;
Step 2 Enter no-negativity constraints in the boxes, which have already been created;
Step 3. Click on ‘Solve’ icon in the ‘Tools’ bar;
Step 4. Fill the blank boxes with the LP information including the constraints;
Step 5. Click ‘OK’ to get the optimal solution for the assignment problem.

Compare your solution with the simplex method ads given below:

We change the model into equations as follows:

Z-40X1-30X2=0
2X1+2X2 +S1= 40
4X1+3X2+S2=120

Now, it is ready to be put in a standard tabular form as follows:

Entering basic variable
BVs Z X1 X2 S1 S2 RHS
Z 1 -40 -30 0 0 0
S1
0 2 2 1 0 40
S2 0 4
3 0 1 120

The most negative coefficient in the objective function is -40 and belongs to X1. As a result, X1
should enter as a basic variable (pivot column). On the other hand, to find the pivot row we have:

Min (40/2, 120/4)= Min (20, 30)= 20
Therefore, S1 should leave the basic position and X1 should enter instead. We will then have:
BVs Z X1 X2 S1 S2 RHS
Z 1 0 10 20 0 800
X1 0 1 1 1/2 0 20
S2 0 0 -1 -2 1 40

As it can be seen, there is no negative coefficient in the objective function and we have the following
optimal solution:

Z= 800
X1=20
X2= 0
S1=0
S2=40
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