Question

Use Simplex Method to solve
Max z= 5x+3y
subject to
x+ y <2
5x+2y <10
3x + 8y <12
and x, y <0​

Answer 1

Answer:

We found in the previous section that the graphical method of solving linear programming problems, while time-consuming, enables us to see solution regions and identify corner points. This, however, is not possible when there are multiple variables. We can visualize in up to three dimensions, but even this can be difficult when there are numerous constraints.

To handle linear programming problems that contain upwards of two variables, mathematicians developed what is now known as the

simplex method. It is an efficient algorithm (set of mechanical steps) that “toggles” through corner points until it has located the one that maximizes the objective function. Although tempting, there are a few things we need to lookout for prior to using it.

Prior to providing the mathematical details, let’s see an example of a linear programming problem that

would qualify for the simplex method:

Example 1

The following system can be solved by using the simplex method:

Objective Function: P = 2x + 3y + z

Subject to Constraints:

3x + 2y ≤ 5

2x + y – z ≤ 13

z ≤ 4

x,y,z≥0