Question

Solve the linear programming problem using the simplex method Maximize P=2x2 + 3x2 + 4x3 subject to X1 + x3 s 12 X2 + x3 s 9 *2, X2, X3 20 Use the simplex method to solve the problem. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. The maximum value of Pis when xy = X2 and x3 = OB. There is no optimal solution

Answer 1

Step 1. Add slack variables 2 Max.P feasible ( ) xit Hats, = 12 X2 + az + S2 = 9 - 2x + 3x2 + 4X3 + ois, to S2 x,, 82, 83, 8, 8230 Stepa. Initial basic salutions are given by x=0=X2 = X3 Si=12 S2 =9 Step 3. Simplex table Step 4. Since, in last table, all Aj 20, this solution is Max p=51 at x, = 12, X2 9, X3 = 0, 28, = 0, S2 = 0 2 d

G 2 3 4 О B Min. Patio CB IXB XI X2 X3 8 & XB/X3 si O 12 1 О 1 1 12 S2 O 1 O 1 P og -2 - 3 - 4 X Blau 3 - OT 0 311 O I - X3 4 1 -- 9 p = 36 Aj Aj-2 o L o O 4 XB/22 XI 2 31 0 23 ų q --- O 0 I q 11 -1 P = 42 Aj o O 2 2. - 2 I O 0 1 I o 3 0 L o - o A P=51 2 3