Consider the following LP. Use revised simplex formula toanswer the questions.
Max Z = -x1 +2x3 +3x4
subject to
x1 -x2+2x3 ?8
4x1 +2x2 +7x3 +9x4 ? 30 2x1 +3x3 +7x4 ? 20 3x1 +x2 -3x3 +4x4 =1 x1, x2, x3, x4 ? 0
a. Show that the basic feasible solution where x1, x2, x3, andx4 is not a feasible solution to the given LP.
b. Show that the basic feasible solution where x1, x3, x4, andthe excess variable of the second constraint (e2) are basicvariables is the optimal solution. Find the values of the decisionvariables and Z in the optimal solution.
c. For which values of the right hand side of the firstconstraint, the current optimal basic feasible solution remainsoptimal?
d. Find the new solution if the right hand side of the firstconstraint is changed to 12. Use dual simplex if necessary.
e. For which values of the objective function coefficient ofx3, the current optimal basic feasible solution remainsoptimal?
f. Find the new solution if the objective function coefficientof x3 is changed to 4. Use revised simplex if necessary
