Your parents are going to knock out the bottom of the entire lengthof the south
ID: 3011517 • Letter: Y
Question
Your parents are going to knock out the bottom of the entire lengthof the south wall of their house and turn it into a green house byreplacing some bottom portion of the wall by a huge sloped piece ofglass (which is expensive). They have already decided they aregoing to spend a certain fixed amount. The triangular ends of thegreenhouse will be made of various materials they already havelying around. The floor space in the greenhouse is only considered usable if theycan both stand up in it, so part of it will be unusable, but theydon't know how much. Of course this depends on how they configurethe greenhouse. They want to choose the dimensions of thegreenhouse to get the most usable floor space in it, but they areat a real loss to know what the dimensions should be and how much usable space they will get.
Explanation / Answer
the cost of wall C: length of wall (l) * width of wall (w)
C = lw now since length of wall is a fixed quantity , everything depends now on width of glass ,so we take a look further into the problem
the angle at which glass is placed determines the length of wall which will be knocked off
height of the wall to be knocked out = H,
angle of glass placement =theta, and
height of parents = h
Usable area, A = l(wcostheta) - l(h/tan theta)
now try to maximize or minimeze theta by differentiating and finding , theta from known values. now we can get height of wall which can be knocked of by calculating w*sintheta
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