Question

Exercise 1. Please use the simplex method to solve the below LP min z=3.r - 12 s.t. 21; +12<8 21 +225 21 - 22 S4 21,220 a) Write the LP in standard form. b) Provide tableaus, BV, NBV, solution, objective value for each iteration of the simplex method. (Hint: the optimal value z=-5).

Answer 1

SO LOTION : mi 2: 3x - 1) Sit. 2x + X₂ <q x+2<5 x,-X2 st "1, H2 20 a Standard form min2= 3x - x₂ + osit OS2 +053 soto 2x + x2 + s = 8 x1 + x2 + S2=5 x-X2 + 3 =4 x,,R2, S1, S2, S320 b. BES x = x2 = 0 75, 8, 52=5, 3=4 M12 Z=0 simplex Table o ci Basis 3 -1 0 CB ry b S2 X2 V Si S3 O SI 8 1 2 5 (5 S2 - 4 - 53 -1 o o 0 zj 3 Cj-zj -1 Here G-j so Herre Not feasible. Pteration I 31 1 3 5 S3 9 zi -1 -1 0-1 0 G-2 0 1 0 Here 0-4 20 Hence feasible. x2 - 2

from the table 2 = 0 X2=5 SI = 3, S2=0, S3 = 9 + zmin =-5