bird traveling to a nest wants to save energy This is a multiple choice question in one of tests I just wrote and I did not know the answer to it. I was just stuck on this during the test. It is a very weird question, one I find to be impossible.
Here it goes:

Scientists have determined some species of birds tend to avoid flights
  over large bodies of water during daylight hours. It is believed that
  more energy is required to fly over water than land because air rises
  over land and falls over water during day. A bird with these
  tendencies is released from an island that is 5 km  form the nearest
  point B on a straight shoreline, flies to point C on the shoreline,
  and then flies along the shoreline to its nesting area D. Assume that
  the brid instinctively chooses a path that will minimize its energy
  expenditure. Points B and D are 13 km apart.
If it takes 2 times as much energy to fly over water as land, what is
  the minimum amount of total energy that the bird could expend
  returning to its nesting area?
a) 2.88 units $\phantom{abcd}$ b) 21.66 units $\phantom{abcd}$ c) 23.00 units $\phantom{abcd}$ d) 27.85 units

I have no idea how to do this question because it makes absolutely no sense to me. I have sat and thought but I just am not getting anywhere.
 A: 
This is a minimization problem, and you have to minimize 
$$E(x) = 2\cdot |AC| + |CD|$$
where $x = |BC|$, with $C \in[B,D]$, $A\hat{B}D=90°$, $|AB|=5$ and $|BD|=13$.
That is, 
$$E(x) = 2 \cdot \sqrt{5^2+x^2}+13-x$$
Take the derivative of this and find the zeros in $[0, 13]$, etc., giving the multiple choice answer (b).
A: Let $x$ be the distance from where the bird starts to $C$.  Using the Pythagorean Theorem, one finds that the distance from $C$ to $D$ is $13-\sqrt{x^2-25}$ . Setting the energy expenditure factor over the shore equal to $a\,{\rm units\over km}$, the energy used is 
$$
E(x)=2ax + a \cdot(13-\sqrt{x^2-25}).
$$
What you need to do is find the minimum value of $E$ over the interval $[5,\sqrt{194}]$ (if the bird  first flies to $B$, then $x=5$ ; if the bird flies straight to $D$, then $x=\sqrt{194}$).
So:
Set $E'(x)=0$ and find any solutions in $[5,\sqrt{194}]$.
Evaluate $E$ at the solutions found above, at $x=5$, and at $x=\sqrt{194}$.
Select the smallest of these numbers.  This will give you the minimum energy expenditure if the energy expenditure over land is $a\,{\rm units\over km}$.
By the way, the problem seems ill-posed, since they did not tell you what the energy expenditure over land was (I presume they took $a=1$).
