Question

Consider the following LP. Use revised simplex formula to answer 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, and x4 is not a feasible solution to the given LP.

b. Show that the basic feasible solution where x1, x3, x4, and the excess variable of the second constraint (e2) are basic variables is the optimal solution. Find the values of the decision variables and Z in the optimal solution.

c. For which values of the right hand side of the first constraint, the current optimal basic feasible solution remains optimal?

d. Find the new solution if the right hand side of the first constraint is changed to 12. Use dual simplex if necessary.

e. For which values of the objective function coefficient of x3, the current optimal basic feasible solution remains optimal?

f. Find the new solution if the objective function coefficient of x3 is changed to 4. Use revised simplex if necessary

Answer 1

and x1,x2,x3,x4,S1,S2,S3,A1,A2,A3≥0

Entering =x4, Departing =A3, Key Element =4

R4(new)=R4(old)÷4

R1(new)=R1(old)

R2(new)=R2(old) - 9R4(new)

R3(new)=R3(old) - 7R4(new)