Question

same question just A through D steps

(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. () 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, it it exists. Maximize P-3xı + 5x2 subject to 2x1 + x2 58 X1 + X2 = 6 X1. X220 (A) Introduce slack, surplus, and artificial variables and form the modified problem. Maximize p=3x + 5x2-M. subject to 2x2 + x2 + 8 X1 + x2+ = 6 X1, X2, S1, ai 20 (B) Write the preliminary simplex tableau for the modified problem and find the initial simplex tableau.

Answer 1

Given Lineare programming pooblem, Maximize P = 3% + 5x2 2x + x 8 Subject to xt xa He, , Xa > 0 Introducing slack and slack and aurtificial vasejables, Max 3X1 + 5x2 + OS MA subject to 2 x + xy + si Р > ni + x2 + A and 21, X2, SI Now construct Ist simplex Cj 5 B 29 table e, 3 -M CB SI A Min Ratio (XB/X2) Si 1 AI M 6 - = 6- I P = -6M -M -M P Pj--M-3 -M-5 0 ra AI a Here entering va guia ble is and leaving basis variable is So, The pivot element is Construct simplese and Table,

cy 3 5 B. CR B no Min Ratio SI Si २ 1 0 22 0 - 6 Pj P-30 5 5 Pj ( po 0 since all Pj (j > 0 optimal solution Therefore, is X1 x 2 11 6 > Maximize 30