
Mark M. answered 06/03/21
Mathematics Teacher - NCLB Highly Qualified
Draw and label a diagram.
x represents the distance from B to Q
C(x) = 5000(√(x2 + 52)) + 3125(8 - x)
Determine C'(x), set equal to 0 to determine minimum.
Guhaad A.
asked 06/03/21A small house was built on an island off a perfectly straight shoreline. The point B on the shoreline that is closest to the island is exactly 5 miles from the island. Eight miles east of B is the closest source of fresh water to the island. A pipeline is to be built from the island to the source of fresh water by laying pipe underwater in a straight line from the island to a point Q on the shoreline between B and the water source, and then laying pipe on land along the shoreline from Q to the source. It costs 5000 dollars per mile to lay the pipe under the water and 3125 dollars per mile to lay pipe on land. How far east of B should Q be located in order to minimize the total construction costs?
Mark M. answered 06/03/21
Mathematics Teacher - NCLB Highly Qualified
Draw and label a diagram.
x represents the distance from B to Q
C(x) = 5000(√(x2 + 52)) + 3125(8 - x)
Determine C'(x), set equal to 0 to determine minimum.
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