Set up the simplex matrix used to solve the linear programming problem. Assume all variables are nonnegative.
Maximize subject to

A)
B)
C)
D)

Question

Set up the simplex matrix used to solve the linear programming problem. Assume all variables are nonnegative. ​
Maximize  subject to
​  ​
A)​ 
B)​ 
C)​ 
D)​

Quizplus · Accepted Answer

The given LP can be written as:

Maximize: 11eb0d3b_9802_6fcc_9790_b1a4d29f17f5_TB1243_11

Subject to:
11eb0d3b_9802_6fcd_9790_656858e3eccb_TB1243_00

We have only one constraint in this LP. The decision variable is eb0d3b3b-9802-6fce-9790-054338734dfe_TB1243_00.

To set up the simplex matrix, we convert the inequality constraint into an equation by adding a slack variable, say s:

11eb0d3b_9802_6fcd_9790_656858e3eccb_TB1243_00 + s = 0

The initial simplex matrix will have two columns: one for the decision variable and one for the slack variable. The coefficients of the decision variable and slack variable in the objective function and the constraint will be the entries in the simplex matrix. We can rewrite the LP as:

Maximize: 11eb0d3b_9802_6fcc_9790_b1a4d29f17f5_TB1243_11

Subject to: 
11eb0d3b_9802_6fcd_9790_656858e3eccb_TB1243_00 + s = 0

Simplex matrix:

|   | eb0d3b3b-9802-6fce-9790-054338734dfe_TB1243_00 | s | RHS |
|---|---|---|---|
| Z | -11 | 0 | 0 |
|   | 1 | 1 | 0 |

The entries in the first row of the simplex matrix are the coefficients of the decision variable and slack variable in the objective function. The entries in the second row of the simplex matrix are the coefficients of the decision variable and slack variable in the constraint. The RHS (right-hand side) column contains the values on the right-hand side of the constraint.

To solve the LP using the simplex method, we perform row operations to pivot the matrix until we find the optimal solution.

Set Up the Simplex Matrix Used to Solve the Linear