Solve the linear programming problem using the simplex metho

Solve the linear programming problem using the simplex method. Maximize P = -x_1 + 2x_2 subject to -x_1 + x_2 lessthanorequalto 2 -x_1 + 3x_2 lessthanorequalto 8 x_1 - 4x_2 lessthanorequalto 10 x_1, x_2 greaterthanorequalto 0 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. The maximum value of P is P = when x_1 = and x_2 = (Simplify your answers.) B. There is no optimal solution.

Solution

Solution:

Maximize p = -x1 + 2x2 subject to
-x1 + x2 <= 2
-x1 + 3x2 <= 18
x1 - 4x2 <= 10

Tableau #1
x1 x2 s1 s2 s3 p   
-1 1 1 0 0 0 2
-1 3 0 1 0 0 18   
1 -4 0 0 1 0 10   
1 -2 0 0 0 1 0

Tableau #2
x1 x2 s1 s2 s3 p   
-1 1 1 0 0 0 2
2 0 -3 1 0 0 12   
-3 0 4 0 1 0 18   
-1 0 2 0 0 1 4

Tableau #3
x1 x2 s1 s2 s3 p   
0 1 -0.5 0.5 0 0 8
1 0 -1.5 0.5 0 0 6
0 0 -0.5 1.5 1 0 36   
0 0 0.5 0.5 0 1 10

Optimal Solution: the maximum value of p = 10;

when x1 = 6, and x2 = 8