## Linear programming using the simplex method

Would you help me with this linear programming problem please.

The answer is simply 200X1 and 100X2. However, I do not how to arrive at this answer using the simplex method of linear programming.

I get to the tableau below. I hope it is correct. I know then that I am supposed to start pivoting. Could someone show me how to get to the final answer.

Cost functions of the two generators. C1 = 0.6X1 C2 = 0.8X2

Demand constraint X1 + X2 = 300

Generator constraints 0 ≤ X1≤ 200
0 ≤ X2≤ 200

minimise π = 0.6X1 + 0.8X2

Simplex method:

1. Convert all inequalities into equalities by adding slack and surplus variables.

X1 + S1 = 200
X2 + S2 = 200
X1 - R1 = 0
X2 - R2 = 0

2. Form what is known as the tableau - the coefficients of the matrices:

BV X1 X2 S1 S2 R1 R2 RHS
S1 1 0 1 0 0 0 200
S2 0 1 0 1 0 0 200
R1 1 0 0 0 1 0 0
R2 0 1 0 0 0 1 0
π -0.6 -0.8 0 0 0 0 0

Regards,

Cyclops

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