# Linear Programming

Provide an appropriate response.

1) Explain the result if the simplex tableau is solved using a quotient other than the smallest non-nega five quotient.

2) Explain why a different slack variable must be used for each constraint when converting

constraints to linear equations.

3) When would the simplex method be used instead of the graphical method?

4) Each solution of a simplex tableau corresponds to

5) What happens if an indicator other than the most negative one is chosen to solve a simplex tableau?

6) A negative number in the rightmost column of a simplex tableau tells you that you have made what kind of error when pivoting?

7) No unique optimtum solution found from a simplex tableau corresponds to

8) You are given the following linear programming problem (P):

Minimize

subject to:

zx1+x2

?4xi +4x2s1

xl -3x2s2

xl O,x2O

1)

2)

3)

4)

5)

6)

7)

8)

The dual of (P) is (D). Which of the following statements are true? a. (P) has no feasible solution and the objective ftmction of (D) is unbounded. b. (D) has no feasible solution and the objective function of (P) is unbounded. Cl The objective functions of both (1') and (D) are unbounded.

d. Both (P) and(D) have optimal soJutions.

e. Neither (P) nor (D) has feasible solutions.

MULTIPLE CHOJCE.

Choose the one alternative that best completes the statement or answers the question.

The initial tableau of a linear programming problem is given. Use the simplex method to solve the problem.

9)

X1X2 X3 12

001

A)Maximumat9forxi 8,x2=2

C) Maximum at 32 for xz = 8, sj =2

B)Maximumat18forx2=8,x32

D) Maximum at 36 for x ? 2, si = 8

#### Solution Summary

Linear programming problems are solved.