A light manufacturing firm is planning a new factory in a rural part of the western United States. A total of 100 employees are to be hired from the 5 surrounding communities. The following table shows the number of (equally) qualified workers available in each community and community location coordinates (in miles).

Community 1 2 3 4 5 Available 70 15 20 40 30 E-W coordinate 0 10 6 1 2 N-S coordinate 0 1 8 9 3 Planners want to choose a factory site that minimizes total employee travel distance. Assume that travel distance is proportional to straight-line distance from community to factory site.

(a) Formulate this location-allocation problem as a constrained NLP.

(b) Use class optimization software to start from reasonable locations and compute at least a local optimum.