Question

(A) Introduce slack, surplus, and artificial variables and form the modified problem, (B) Write the preliminary simplex tableau for the modified problem and find the initial simplex tableau. (C) Find the optimal solution of the modified problem by applying the simplex method to the initial simplex tableau (D) Find the optimal solution of the original problem, fit exists Maximize P 4x1.5x2 subject to 2x1 + x2 28 X] + xy =21 X1, X220 ntents access access (A) Introduce slack, surplus, and artificial variables and form the modified problem, Maximize p= 4x + 5xz-M 2xy + x2-28 Library subject to orrect ptions X1 +*2* = 21 X1.X2. S1. a 20 Resources

Answer 1

P = 404 + +52 24 + 2 €25. 4+ M = 21 224 + H2 + 8 = 251 y the tax =21 Mar, S., 970.

Iteration-1 Cj 4 5 0 -M MinRatio B CB XB xi X2 Si 41 25 Si 0 25 25 N 21 41 -M 21 (1) 0 1 21 - Z= -21M -M -M -M 2; 2 - C; -M-4 -M-51 0 Negative minimum 2; -C; iS-M-5 and its column index is 2. So, the entering variable is Xz. Minimum ratio is 21 and its row index is 2. So, the leaving basis variable is 41- : The pivot element is 1. Entering = X2, Departing = 4), Key Element = 1 + R2(new) = R2(old) + Ri(new) = R1 (old) - Rz (new)

Iteration-2 C 4 in 0 B Св XB xi 22 Si MinRatio Si 0 4 1 0 1 X2 5 21 0 Z= 105 Z; 5 5 0 Z; - C; 1 0 0

Finally, Since all Zj-Cj≥0

Hence, the optimal solution has arrived with the value of variables as :
x1=0,x2=21

And Max P = Z =105 .