# Linear Programming : Simplex Method, pivoting and maximizing

1. Consider the following linear programming problem:

Maximize 10x + 7y subject to:

X + 3y (less than or equal to symbol) 10

2x -y (less than or equal to symbol) 8

x (greater than or equal to symbol) 0, y (greater than or equal to symbol) 0

The initial simplex tableau is:

(for choices, please see attachment)

2. The particular solution corresponding to the simplex tableau (see attachment) is:

a. x = 2, y = 6, u = 10, v = 0, M = 0

b. x = 2, y = 6, u = 0, v = 0, M = 10

c. x = 6, y = 0, u = 2, v = 0, M =10

d. x = 6, y = 0, u = 6, v = 0, M = 10

e. none of the above

3. The result of pivoting the simplex tableau (see attachment) about -2 (1st row, 1st column) is:

(for choices, please see attachment)

4. Consider the simplex tableau (see attachment). The tableau is the final one in a problem to maximize x + 2y + 3z.

The maximum value of x + 2y + 3z is:

a. -19

b. -12

c. 0

d. 19

e. none of the above

5. In the following simplex tableau, the next pivot element is (see attachment for tableau):

a. 4 in the second row, first column

b. -3 in the third row, first column

c. 8 in the second row, fourth column

d. 1 in the first row, second column

e. none of the above

6. Consider the following linear programming problem:

Maximize 3x -y subject to:

6x -5y (less than or equal to symbol) 24

x + 9y (greater than or equal to symbol) 63

x (greater than or equal to symbol) 0

y (greater than or equal to symbol) 0

Which of the following is the initial simplex tableau?

(for choices, please see attachment)

#### Solution Summary

Linear programming problems are solved. Pivoting and maximizing values are investigated.