A holding pen is being built alongside a long building. The pen requires only three fenced sides, with the building forming the fourth side. There is enough material for 90m of fencing.
- Predict what dimensions will give the maximum area of the pen and write a function to model the area.
I'm entirely sure how to start off this question, any tips or suggestions would be greatly appreciated.
We'll call our sides of the fence $x$ and $y$. We want to maximize the area of (I'll assume) the rectangle that this fence forms. The area is then $xy$. However, we are held to the constraint that we use only 90m of fencing, so the perimeter, not including the building is $x+2y = 90$.
Now solve for either $x$ or $y$ and substitute it into your objective function $xy$. Then use basic calculus to find the max.
Really you don't even need calculus. You are just finding the vertex of that parabola which you can do with even more elementary, but probably more tedious means.