Use the simplex method for solving nonstandard problems to solve the given linear programming problem.

Question

Quizplus · Accepted Answer

The given linear programming problem can be expressed as:

Maximize P = 6x + 3y
Subject to:
2x + y ≤ 15
x + 3y ≤ 18
x, y ≥ 0

Setting up the initial simplex tableau:

|   |  x |  y | s1 | s2 | P |
|---|---|---|---|---|---|
|s1 | 2 | 1 | 1 | 0 | 0 |
|s2 | 1 | 3 | 0 | 1 | 0 |
|Z  |-6 |-3 | 0 | 0 | -1|

The pivot is at row 1, column 1 (the smallest ratio of P/s1 and P/s2).

|   |  x |     y |     s1 |     s2 |      P |
|---|---|------|------|------|--------|
|s1 | 1 | 1/2 |  1/2 |  0    |  0     |
|s2 | 0 | 5/2 | -1/2 |  1    |  0     |
|Z  | 0 | 9/2 |  3   |  0    | -1/2 |

The pivot is at row 2, column 2.

|   | x |   y |   s1 |   s2 |    P |
|---|---|----|----|----|------|
|x  | 1 | 1/5| 1/5 | 0    | 0     |
|s2 |-3| 0   | 1/5 | 1   | 0     |
|Z |15/5| 0   | 3/5 | 0     | -11/5|

Thus, the optimal solution is x = 5, y = 3, and P = 11. Therefore, option D is the best choice.

Use the Simplex Method for Solving Nonstandard Problems to Solve