I sat for an exam a few days ago. I managed to answer every question except for question $1$c in the calculus paper. Provided that I got question $2$d correct (my answer was $m=0.5$), the absence of an answer for question $1$c should not in any way affect my overall grade. Out of interest, however, I am wondering if you could start me off on how to approach problem $1$c. Both the questions can be found below.
Thank you very much.
Question $1$c:
An enclosure at a reserve is divided into two rectangular cages.
One side of the enclosure is a solid wall.
There is a fence around the rest of the enclosure and another between the male and female cages.
The total length of the fences is $275$ m.
$5$ male birds are kept in the smaller cage and $8$ female birds in the larger cage.
The males have an average area of $250$ sq.m each in their cage.
The area of the female cage is to be maximised.
Find the average area for each of the female birds in their cage.
Question $2$d:
The diagram below shows part of the graph of the function $y=x^2, x>0$.
The shaded region between the curve and the $X$-axis, and between $x = m$ and $x = m + 2$, has an area of $5 \frac16$ sq.units. Find the value of $m$.
Explain the choice of the solution.