Extreme vertices designs

Mixture designs that cover only a subportion or smaller space within the simplex. These designs must be used when your chosen design space is not an L-simplex. The presence of both lower and upper bound constraints on the components often create this condition. For example, you need to determine the proportions of flour, milk, baking powder, eggs, and oil in a pancake mix that would produce an optimal product based on taste. Because previous experimentation suggests that a mix that does not contain all of the ingredients or has too much baking powder will not meet the taste requirements, you decide to constrain the design by setting lower bounds and upper bounds.

The goal of an extreme vertices design is to choose design points that adequately cover the design space. The illustration below shows the extreme vertices for two three-component designs with both upper and lower constraints:

The light gray lines represent the lower and upper bound constraints on the components. The dark gray area represents the design space. The points are placed at the extreme vertices of design space.