We form a rt triangle:
X = 200 Ft. = hor side = Width of river.
Y = 600 Ft.=Ver. side=dist. dwn stream.
Z = sqrt((200)^2+(600)^2) = 632.5 Ft.
= hyp. = Shortest dist. across river.
If the X-Y route is taken:
Cost = 50*200 + 30*600 = $28,000.
If the Z route is taken:
Cost = 50 * 632.5 = $31,625.
The X-Y route is cheaper.
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.
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