As shown in the accompanying left-hand figure, three cities are to receive water from one...

As shown in the accompanying left-hand figure, three cities are to receive water from one well field, which is yet to be developed. The location of the well field is to be determined. City 1 is to receive 1.0 million gallons per day, city 2 is to receive 2.0 MGD, and city 3 needs 3.0 MGD. The cost of delivery can be found from the right-hand figure, where cost is giving in units of $1000 per mile of pipe, depending on flow quantity.

Map coordinates (in miles) of cities 1–3 are (15, 40), (12, 10), and (50, 20), respectively.

The distance between two points i and j is given by

(a) Write the objective function with constants substituted where appropriate.

(b) What problems do you sec in solving the simultaneous partial derivatives?

(c) Determine the solution by spreadsheet enumeration, using a grid size of one mile by one mile. What are the hest coordinates for the well field?