A water line is to be built from point P to point S and must pass through regions where construction costs differ (see figure). The cost per kilometer in dollars is 3k from P to Q, 2k from Q to R, and k from R to S. For simplicity, let k = 1. Use Lagrange multipliers to find x, y, and z such that the total cost C will be minimized.

Transcribed Image Text:

2km 1km KXY → R ・10km S