Question

Solve the linear programming problem using the simplex method. Maximize z = 2X, + 5x, subject to 5x, + X560 5x + 2x2 580 X1 + x2 $70 X1, X2 20. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The maximum is z = when X, x2 = 1,5, - S2 = and s3 = B. There is no maximum solution for this linear programming problem.

Answer 1

бо, 5 +1, + 5) 5 +2 4, + 5, - Хо th, * 3 го 4, , ,.

Negative minimum Zj-Cj is -5 and its column index is 2. So, the entering variable is x2.

Minimum ratio is 40 and its row index is 2. So, the leaving basis variable is S2.

∴ The pivot element is 2.

Iteration-1 C 2 5 0 MinRatio хв B CB XB 21 X2 $ $2 S; X2 60 si 60 1 1 0 0 = 60 80 S2 0 80 5 (2) 0 1 0 40 2 S3 0 70 1 1 0 0 1 70 1 70 Z = 0 2 0 0 0 0 0 Z-C; 2 -51 0 0 0

Iteration-2 C 2 5 0 0 0 B XB Xı X, si S, S; MinRatio Si 20 2.5 0 1 -0.5 0 X2 in 40 2.5 0 0.5 0 S3 0 30 -1.5 15 00 -0.5 1 Z= 200 Z; 12.5 0 5 o 2.5 00 2.5 Z; - C; 10.5 0

Hence, optimal solution is arrived with value of variables as :
x1=0,x2=40,s1=20,s2=0,s3=30

Max Z=200