SOLUTION: A new house is built across the river which is 292 yards downstream from the nearest telephone relay station. The river is 96 yards wide. In order to wire the house for phone servi

Question 799143: A new house is built across the river which is 292 yards downstream from the nearest telephone relay station. The river is 96 yards wide. In order to wire the house for phone service, wire will be laid across the river under water and along the edge of the river above ground. The cost to lay wire under water is $32 per yard and the cost to lay wire above ground is $14 per yard. How much wire should be laid ON LAND to minimize the cost?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A new house is built across the river which is 292 yards downstream from the nearest telephone relay station.
The river is 96 yards wide. In order to wire the house for phone service, wire will be laid across the river under water and along the edge of the river above ground.
The cost to lay wire under water is $32 per yard and the cost to lay wire above ground is $14 per yard.
How much wire should be laid ON LAND to minimize the cost?
:
Let x = the length of the cable under the water
The cable under the water would be the hypotenuse of a triangle with legs of
96 and x times $32
The cable on the land would be (292-x) times $14
The equation, cost = f(x)
f(x) = 32() + 14(292-x)
Graphically

minimum cost occurs when x = 47 yds,
292 - 47 = 245 yds laid on the land
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