4-4-7 work through the simplex method step by step(in tabular form) to solve the following problem
Maximize Z=2x1-x2+x3
subject to
3x1+x2+x3<=6
x1-x2+2x3<=1
x1+x2-x3<=2
and
x1,x2,x3>=0
4-6-2 consider the following problem
Maximize Z=4x1+2x2+3x3+5x4
subject to
2x1+3x2+4x3+2x4=300
8x1+x2+x3+5x4=300
and
xj>=0, for j=1,2,3,4
(a) using the big m method, construct the complete first simplex tableau for the simplex method and identify the corresponding initial(artificial) BF solution. Also identify the initial entering basic variable and the leaving basic variable
(b)work through the simplex method step by step to solve the problem
(c)using the two-phase method,construct the complete first simplex tableau for phase 1 and identify the corresponding initial BF solution, Also identify the initial entering basic variable and the leaving basic variable
(d)work through phase 1 step by step
(e)construct the complete first simplex tableau for phase 2.
(f)work through phase 2 step by step to solve the problem.
(g)compare the sequence of BF solutions obtained in part (b) with that in parts (d) and (f). which of these solutions are feasible only for the artificial problem obtained by introducing artificial variables and which are actually feasible for the real problem?
(h)use a software package based on the simplex method to solve the problem.
4-6-7
Maximize Z=2x1+5x2+3x3,
subject to
x1-2x2+x3>=20
2x1+4x2+x3=50
and
x1,x2,x3>=0
Same as 4-6-2's
4-6-17 consider the following problem
Maximize Z=4x1+5x2+3x3
subject to
x1+x2+2x3>=20
15x1+6x2-5x3<=50
x1+3x2+5x3<=30
and x1,x2,x3>=0
work through the simplex method step by step to demonstrate that this problem does not possess any feasible solutions.
Maximize Z=2x1-x2+x3
subject to
3x1+x2+x3<=6
x1-x2+2x3<=1
x1+x2-x3<=2
and
x1,x2,x3>=0
4-6-2 consider the following problem
Maximize Z=4x1+2x2+3x3+5x4
subject to
2x1+3x2+4x3+2x4=300
8x1+x2+x3+5x4=300
and
xj>=0, for j=1,2,3,4
(a) using the big m method, construct the complete first simplex tableau for the simplex method and identify the corresponding initial(artificial) BF solution. Also identify the initial entering basic variable and the leaving basic variable
(b)work through the simplex method step by step to solve the problem
(c)using the two-phase method,construct the complete first simplex tableau for phase 1 and identify the corresponding initial BF solution, Also identify the initial entering basic variable and the leaving basic variable
(d)work through phase 1 step by step
(e)construct the complete first simplex tableau for phase 2.
(f)work through phase 2 step by step to solve the problem.
(g)compare the sequence of BF solutions obtained in part (b) with that in parts (d) and (f). which of these solutions are feasible only for the artificial problem obtained by introducing artificial variables and which are actually feasible for the real problem?
(h)use a software package based on the simplex method to solve the problem.
4-6-7
Maximize Z=2x1+5x2+3x3,
subject to
x1-2x2+x3>=20
2x1+4x2+x3=50
and
x1,x2,x3>=0
Same as 4-6-2's
4-6-17 consider the following problem
Maximize Z=4x1+5x2+3x3
subject to
x1+x2+2x3>=20
15x1+6x2-5x3<=50
x1+3x2+5x3<=30
and x1,x2,x3>=0
work through the simplex method step by step to demonstrate that this problem does not possess any feasible solutions.