Managers at Office Products, Inc. are planning their sales campaigns for the coming year. As one part of this effort, they are attempting to determine the relationship between the number of sales reps that are assigned to a product and the sales of that product. The subjective estimates of a group of experienced managers are summarized in the following table, which relates sales effort to sales:

a. Build a least squares model to fit an S-shaped curve to this data set. An appropriate function has the form

What values of the four parameters a, b, c, and d minimize the sum of squared differences between the model’s predicted values and the observations? (Good initial solutions for the four parameters are helpful in achieving a good fit.) In general, the parameter b represents the lowest level of the function and a its highest level.

b. Determine whether there are local optima in the optimization problem in part (a) by providing Solver different initial values for the four parameters.