Electric power for a community on one bank of a straight river 0.5 km wide must come from a power station on the opposite bank of the river 6 km downstream. It costs $1500 /km to lay cable on land and $2400 /km to lay cable underwater. What path should be selected to minimize cost? Illustrate with a diagram. Provide your answer to the nearest metre. Include domain restrictions and use the extreme values algorithm to verify that a minimum cost has been found.