Question

Help me pls I need the answer

Answer 1

By using given equation the maximum is 8 when
`x_1` = 2 and
`x_2` = 0;
`s_1` = 2,
`s_2` = 0, and
`s_3` = 0. The correct option is A.

A linear programming problem that can be solved using the simplex method. The problem is as follows:

Maximize:
`(z = 2x_1 + x_2)`

Subject to:

`(x_1 + 5x_2 \le 12)`

`(2x_1 + 2x_2 \le 4)`

`(x_1 + 3x_2 \le 4)`

`(x_1 \ge 0, x_2 \ge 0)`

Convert the problem into a standard form by introducing slack variables.

Find the initial tableau.

Choose the pivot column and pivot row.

Perform the pivot operation.

Repeat steps 3 and 4 until all constraints are satisfied or the objective function is maximized.

In this case, the initial tableau is as follows:

`x_1`
`x_2`
`s_1`
`s_2`
`s_3` RHS

z -2 -1 0 0 0 0

`s_1` 1 5 1 0 0 12

`s_2` 2 2 0 1 0 4

`s_3` 1 3 0 0 1 4

After performing a few pivot operations, we get the final tableau:

`x_1`
`x_2`
`s_1`
`s_2`
`s_3` RHS

z 0 0 1 2 1 8

`x_1` 1 0 0 1/2 1/2 2

`s_2` 0 2 0 1/2 -1 0

`s_3` 0 1 0 -1/2 1/2 0

From the final tableau, we can see that the maximum value of z is 8 when
`x_1` = 2 and
`x_2` = 0.

The slack variables
`s_1, s_2`, and
`s_3` are all 0.

Therefore, the correct answer is A.