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A construction crew has to dig ditches for a set of pipes that must carry wat ...
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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 \( 3 \mathrm{~km} \) apart and point \( A \) is \( 3 \mathrm{~km} \) 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 \( \mathrm{D} \) along the midline a distance \( h \) from the midpoint of \( \mathrm{B} \) and \( \mathrm{C} \). They know that they should choose \( h \) satisfying \( 0 \leq h \leq 2 \) but they are not sure exactly what value of \( h \) to use. a) Formulate an expression \( L(h) \) for the total length of ditch. \[ L(h)= \] (2 points.) 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. \( h= \) (3 points.)