Simplex Method/Examples/Arbitrary Example 1

Examples of Use of Simplex Method

Consider this exercise in linear programming:

Let it be required to find the minimum of the function:

$\map U {x, y} = 4 x + 3 y$

subject to the conditions:

\(\ds x + y\)

\(\le\)

\(\ds 20\)

\(\ds 3 x + y\)

\(\le\)

\(\ds 30\)

\(\ds x\)

\(\ge\)

\(\ds 0\)

\(\ds y\)

\(\ge\)

\(\ds 0\)

The maximum feasible value of $U$ is given by:

$U = 65$

The simplex is the shaded region in the following diagram:

and the optimizing vertex is $E$.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): simplex method
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): simplex method