1. ## problems about application of differentiation

A rectangular pen, with 3 partitions, is to be built with 180m fencing. Which of the following dimensions of the pen will give the maximum possible area?

A. 50m by 16m
B.45m by 18m
C. 65m by 10m
D. 50m by 18m

I thought it's D, but it's not. How should I start for this question?

2. What do you mean by three partitions?

3. i also don't really get it ....
i guess ...it's like the following.....

4. Originally Posted by wintersoltice
i also don't really get it ....
i guess ...it's like the following.....

If that's it, you want to maximize the expression $LW$, where $L$ is the length and $W$ is the width, subject to the constraint $2L+4W=180$.

Solve for $L$: $L=90-2W$

Plug back into the original equation: $W(90-2W) = 90W-2W^2$ - this is the equation you want to maximize.

Take the derivative, set it equal to $0$, and solve for $W$: $90-4W=0 \implies W=22.5$ and $L=45$, which is not a choice, so the interpretation of the picture can't be correct.

In fact, I don't think any of the choices agree with the picture, as the equation $2L+4W=180$ is not solved by any of the 4 choices.

5. since the previous interpretation is not correct....
then if add one more line as width.....