Question: 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

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.

2km 1km KXY R 10km S

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