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help with calculus project?
We're studying mathematical modeling and optimization or maximization. I'm having a difficult time with this project:
Building a Greenhouse
Your parents are going to knock out the entire length of the south wall of their house and turn it into a greenhouse by replacing the 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 fixed amount. The triangular ends of the greehouse 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. They want to choose the dimensions of the greenhouse to get the most usable floor space. What should the dimensions of the greenhouse be and how much usable space will your parents get?
(end)
Now my first instinct is to use length x width x height (1/2) but I was told I should be using trig (sin,cos,tan) I don't know how to start this.
3 Answers
- Anonymous1 decade agoFavorite Answer
I assume the length ("L") and width ("W") of glass is constant, and the minimum usable height is "dad's" height, call it "f".
Essentially, what will vary is the angle you place the glass in relation to the house. Your goal is to get the usable length out from the house as large as possible, in relation to the entire length from house to glass. The height from glass to ground will vary from "f" to the length of the glass, "L".
Interesting problem.. I'll think about it some more..
- 1 decade ago
I don't exactly get the question. However, this is a perimeter vs area question. It's very basic. Cost = price * perimeter. You know the fixed amount of money they can spend and replace C with it. A = L * W. You use the cost formula to isolate one of the variables. Then sub in the equation for the isolated variable and then you optimize by finding the vertex. Then you sub that value back in to the cost formula and find the other variable.
- CurlyLv 61 decade ago
A much more entertaining problem is the minimization of conductive heat loss with an insulating jacket around a pipe. Theres an optimal size for minimal losses. Its cool. Its something to check out.