A construction crew has to dig ditches for a set of pipes that must carry water from point A to both of points B and C (see figure). Points B and C are 3 km apart and point A is 3 km from the midpoint of B and C. They want to dig as little as possible and they believe the best way to do that is to dig from point A to some point D along the midline a distance h from the midpoint of B and C. They are not sure exactly what value of h to use. B 3 km D 3 km C h (a) Formulate an expression L(h) for the total length of ditch. L(h) = (b) Now calculate the value of h which minimizes the amount of ditch to be dug. If there is more than one such value, give your answer as a comma-separated list. h = km Note: You do not need a calculator to solve this problem.