Hello,
I was wondering if you could help me with a problem that I posted on this forum a few days ago:
http://www.mathhelpforum.com/math-he...area-help.html
Tom gave me a link to a similar problem that you helped someone with, so I was wondering if you could assist me as well (I get a little confused with "balloon calculus."
I had already written my problem with different variables than those that Tom suggested. I have:
x=height of the wall (rather, the vertical distance between the sloping glass pane and the ground)
p=height of my tallest parent
w= the entire length of the floor
z=the length of the floor that will make up the usable space
t=the length of the floor that will be part of the unusable space
So, w is then equal to z+t.
and, finally, y=the width of floor.
The relationships I have are p/t=x/w where, again w=z+t
So, if I understand this correctly and am setting out the problem correctly, I am trying to maximize yz, which is the usable floorspace.
So, the first thing I did was find z in terms of x, p, and t. I'm not sure if this step is necessary, but I got z=(xt)/(p+t).
So, I know that the area will be equal to yz which equals y((xt)/(p+t)). I'm not really sure where to go from here. I know eventually I need to take the derivative, set it equal to zero, and find the value that will maximize that. I'm just not clear how to go about doing it, since there are so many variables and no actual numbers.
Should I find y in terms of the other variables? How would I do that?
I would really appreciate it if you could give me a hand.
Thanks!
