The following shows a series of measurements of the height (in inches) of a new genetically engineered tomato plant versus the number of weeks after the plant was replanted outdoors.

Week 1 2 4 6 8 10 Height 9 15 22 33 44 52 Researchers wish to fit this experience with an S-shaped logistics curve size =

k 1 + ea + b1weeks2 where k,

a, and b are empirical parameters.

(a) Formulate an unconstrained NLP to fit this form to the given data so as to minimize the sum of squared errors.

(b) Use class optimization software to compute at least a local optimum for your curve fitting model starting with k = 50, a = 3, b = -0.3.