The state highway department would like to have a formula for estimating the snow removal cost of each snow event as a function of the number of inches of snow to fall. A sample of n falls fj and corresponding removal costs cj, j = 1,c, n, has been collected from history. Now the department would like to fit these data to an S-shaped curve of the form c =

k 1 + ea + bf in a way that minimizes the sum of squared errors.

Here k,

a, and b are empirical parameters of arbitrary sign.

(a) Explain why the decision variables in this optimization problem are k,

a, and b.

(b) Formulate an unconstrained optimization model to perform the desired curve fit.

(c) Is your model best classified as an LP, an NLP, an ILP, or an INLP, and is it singleor multiobjective?