## Mathcad and Optimisation

Last Updated on Saturday, 21 April 2012 17:12 Written by Evanish Thursday, 09 December 2010 14:34

**Mathcad and Engineering Optimisation**

Optimisation is aimed at finding the best available values of some objective function given a defined domain, including a variety of different types of objective functions and different types of domains. It is often used extensively in the fields of mathematics and computer science. Mathcad is extremely useful in the field of solving and optimisation. It offers a range of functions to solve linear and nonlinear equations and systems of equations. The Find, Maximize, Minimize, and Minerr functions are used primarily within solve blocks, allowing for natural notation. The remaining functions can be used within programs for iterative calculations or on their own in a single expression.

Let’s take a look at example of where Mathcad is used to solve constraint non-linear optimization problem.

**Maximize and minimize the following function**

subject to the constraint that (x,y) falls within the right triangle T with vertices (0,0), (9,0) and (0,9).

**3D Plot of function**

**Graph the feasible region in the x-y plane**

**In order to solve the problem we will use guess values to find the 3 points of interest**

**Now solve for the maximum**

**Creating a scatter plot on top of the original plot shows the validity of the solution:**

If you wish to find the overall maximum of the function without constraints then Maximize (or Minimize) can be used by itself without a solve block.

Mathcad was able to easily compute this particular optimisation question quickly and efficiently and was also able to take into consideration constraints placed on optimisation. This is particularly useful in the mathematics and computer science industries as fast and efficient tools are required for use in research and optimising profits and minimising loses in any number of industries.

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