# Thread: HELP! weird optimize problem.

1. ## HELP! weird optimize problem.

Hello everyone,

I almost done with all the homework from my calculus class, but I got stuck on one problem, only one problem, but very difficult to understand.
I would really appreciated if someone helps me with it. I dont even know how to start it : /
here it goes...

" Your neighbors are going to knock out the bottom of the entire lenght of the south wall of their house and turn it into a green house by replacing some bottom portion of the wall by a huge sloped piece of glass(which is expensive). They have already decided they are going to spend a certain fixed amout. The triangular ends of the greenhouse will be made of various materials they already have lying around.

The floor space in the greenhouse is only considered usable if they can both stand up in it, so part of it will be unusable, but they dont know how much. Of course this depends on how they configure the greenhouse. They want to choose the dimentions of the greenhouse to get the most usable floor space in it, but they are at a real loss to know wha the dimensions should be and how much usable space they will get. Fortunately, they know you are taking calculus. Amaze them!""

2. Originally Posted by ((ECHO))
Hello everyone,
...
" Your neighbors are going to knock out the bottom of the entire lenght of the south wall of their house and turn it into a green house by replacing some bottom portion of the wall by a huge sloped piece of glass(which is expensive). They have already decided they are going to spend a certain fixed amout. The triangular ends of the greenhouse will be made of various materials they already have lying around.

The floor space in the greenhouse is only considered usable if they can both stand up in it, so part of it will be unusable, but they dont know how much. Of course this depends on how they configure the greenhouse. They want to choose the dimentions of the greenhouse to get the most usable floor space in it, but they are at a real loss to know wha the dimensions should be and how much usable space they will get. Fortunately, they know you are taking calculus. Amaze them!""
Hello,

I'm not quite certain that I understand your problem correctly.
I've attached a sketch of the situation as I understand it. Is it this what you want to calculate?

The green area is the usable part of the floor (maximum), the blue area is the area of glass (fixed value), h is the length of the neighbour and W is the width of the base of the greenhouse.

Everything OK so far?

3. Originally Posted by earboth
Hello,

I'm not quite certain that I understand your problem correctly.
I've attached a sketch of the situation as I understand it. Is it this what you want to calculate?

The green area is the usable part of the floor (maximum), the blue area is the area of glass (fixed value), h is the length of the neighbour and W is the width of the base of the greenhouse.

Everything OK so far?
Yeah, that makes sense. Thats how I did the sketch too. What confuses me the most is what the probles is asking for. For example, "greenhouse is only considered usable if they can both stand up in it." How can I know how tall are they? they could be from 5ft to 6 ft tall.
And also this part, "choose the dimentions of the greenhouse to get the most usable floor space in it". They probably want some kind of equation, because theres no numbers to work with, right?
Eatboth, thank you so much for your help.

4. im lost.

5. They want to choose the dimensions that can give them the most usable space (space tall enough so they can stand up). How can I make up a formula that mix the anlge of the glass, the dimensions of the inner rectangle(where they walk around) and the height of the greenhouse? is that possible?