Applied Calc - An underground electricity cable is to be laid between two boat docks on opposite banks of a river. One boat dock is 600 feet downstream from the other. The river is 200 feet wide. If the cost of laying the cable is $50 per foot under water and $30 per foot on land, how should the cable be laid to minimize the cost to connect the two docks? Also, find the minimum cost to lay such a cable.

Question

Applied Calc - An underground electricity cable is to be laid between two boat docks on opposite banks of a river.  One boat dock is 600 feet downstream from the other.  The river is 200 feet wide.  If the cost of laying the cable is $50 per foot under water and $30 per foot on land, how should the cable be laid to minimize the cost to connect the two docks?  Also, find the minimum cost to lay such a cable.

anonymous · Answer

|dw:1332954978326:dw|So we can either do a direct path (all underwater) from 1 dock to the other, or a mixture of land cable and underwater cable to connect the two.  Calling l the length of land cable and w the length of underwater cable, the total cost can be expressed as:
C=30l+50w