math

posted by .

You are asked to design a piping system that will connect a drilling rig 12 miles offshore to refinery on shore 20 miles down the coast. What values of x and y will give the least expensive connection if underwater pipe (x-section) costs $50.000 per mile and land-based pipe (y-section) costs $30.000 per mile?

  • math -

    Draw a diagram. Let P be the point on shore where the pipe goes underwater.

    Then if D is the drill rig, and R is the refinery,

    x^2 = 12^2 + (20-y)^2
    and the cost is
    c = 50x+30y
    c = 50√(144 + (20-y)^2) + 30y

    dc/dy = 50(y-20)/√(y^2 - 40y + 544) + 30
    dc/dy=0 when

    y = 11
    so, x = 15

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus

    Optimization An offshore oil well is 2km off the coast. The refinery is 4 km down the coast. Laying a pipe in the ocean is twice as expensive as on land. What path should the pipe follow in order to minimize the cost?
  2. Calculus

    A man is in a boat 4 miles off a straight coast. He wants to reach a point 10 miles down the coast in the least possible time. If he can row 4 miles per hour and run 5 miles per hour, where should he land the boat?
  3. Math(module 4 Calculus)

    (minimum commuting time) A lighthouse lies 2 miles offshore directly across from point A of a straight coastline. The lighthouse keeper lives 5 miles down the coast from point A.What is the minimum time it will take the lighthouse …
  4. Calculus

    An offshore well is 2 miles off the coast. The refinery is 4 miles down the coast. If a laying pipe in the ocean is twice as expensive as on land, what path the pipe should follow in order to minimize the coast. Is the answer 2.1?
  5. Calculus

    You are in a boat "a" miles from the nearest point on the coast. You are to go to a point Q, which is "b" miles down the coast and 1 mile inland. You can row at 2 miles per hour and walk at 4 miles per hour. If a=3, and b=4, toward …
  6. calculus

    Given ensuing information, determine the least cost and the least cost mix of on- and off-shore pipe. The intake facility is in the water 2 miles vertically north of the shoreline The water filtration plant is on land 1 mile vertically …
  7. math

    a man is in a boat 2 miles from the nearest point on the coast. He is to go to point q, 3 miles down the coast and 1 mile inland. If he can row at 2 mi/h and walk 4 mi/h toward what point on the coast should he row in order to reach …
  8. Calculus

    An offshore oil well is 4 kilometers off the coast. The refinery is 5 kilometers down the coast (see figure). Laying pipe in the ocean is twice as expensive as on land. What path should the pipe follow in order to minimize the cost?
  9. math

    one day a sailor was sailing 32 miles from the shore. he then went 22 miles east then 67 miles north. How far did he travel straight?
  10. Calculus (trig derivatives)

    A lighthouse 2 miles offshore has a light that rotates once every 20 seconds. At what rate is the light traveling along the shore if it is shining on a point 4 miles along the shore from the point nearest the lighthouse?

More Similar Questions