Extreme vertices designs are 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 design. 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 mixture that would produce an optimal product based on flavor. Because previous experimentation indicates that a mixture that does not contain all the ingredients or has too much baking powder will not meet the flavor 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 following figure shows the extreme vertices for two three-component designs with both upper and lower constraints: