The problem of constructing nonsingular saturated optimal designs (i.e. optimal designs with the number of support points which is equal to the number of parameters) is quite important since the use of such designs allows to decrease experimental expenses. On the other hand, excess optimal designs (i. e. optimal designs with the number of support points which is greater than the number of parameters) are useful in practice too, since they can be used to verify the adequateness of the model. For a rational two-dimensional nonlinear in parameters model used in analytical chemistry, we investigate how homothetic transformations of the design space affect the number of support points in the optimal designs. We show that there exist two types of optimal designs: a saturated design and an excess design. The saturated optimal designs are constructed explicitly. Numerical methods for constructing excess optimal designs are used.