Question

Please use the big M method to solve the following linear program. Write down all tableau, note basic variables and nonbasic variables. Use slack and artificial variables. Construct your tableau iterations using the standard form of the program. For example first line z+2x1-2x2+2x3=0. If possible, STATE THE OPTIMAL SOLUTION AND THE OPTIMAL VALUE. Otherwise state why you cannot find them.

Consider the following linear program: 2x3 max z= –2x1 + s.t. + -x1 21 > 0, 2x2 - 2x2 + + x2 > 0, x3 > 03 > -1 0

Answer 1

solation or max2 = -289 +2212 - 20g st 24 +242 + x3 = 4 +29+ 8g 2nd see, 2d, 292,0 Standard for max2 = -229,7242-200 g tosi-mai-maa st 224 +222 + seg at A, = 4 -29 4 2 3 = 82 + Aaaa2 24, H2, H3, A, , A2, Jaso where ALIA2 ase artifical variable Sa is surplus variable 1

PROBLEM: -M -M C -2 2 -2 0 Var | X1 X2 X3 S2 A1 2 2 1 0 A2 -1 0 1 -1 Z -M -2M-2M M C-1-2+M 2+2M 2+2 -M M A1 1 0 M 0 M A2 0 4 1 -1 M Z = 0 1 0 0 0 Iteration: C | -2 2 -2 0 -M -M | Var X1 X2 X3 S2 A1 A2 -M | 11 | 2 2 1 10 | 110 | 4 | 2 -M A2 -1 0 1 -1 0 1 -1 0 Z -M -2M-2M M M M Z = -3M c-z |-2+M 2+2M 242 M 0 0 1 key column 4 key row 3 key element 2.0 Iteration: 2 -M C | -2 2 Var X1 X2 X2 1 1 | A2 -1 0 Z 2+M 2 C-Z -4-M 0 -2 X3 1/2 1 1-M -3+M 0 S2 O -1 M -M -M -M | A1 A2 1/2 0 2 4 0 1 -1 -1 1 - M Z = 4+M. -1-M 0 key column 5 key row 4 key element 1.0 Iteration: C -2 2 Var x1 X2 2 X2 | 3/2 1 -2 X3 -1 0 Z 5 2 C-Z -7 0 -2 0 M M X3 S2 A1 A2 0 1/2 1/2-1/25/ 20 1 -1 0 1 -1 0 -2 3 1 -3 Z = 7 0 -3 -1-M 3-M | Solution: X2 = 2.5 X3 = -1.0 Z = 7.0