- #1
don1231915
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Optimization under differentiation!
OK
I have a upside down looking curve structure (½ ellipse). It has the following specifications:
The building has a rectangular base 150m long and 72m wide. The max height of the structure should not exceed 75% of its width or be less than half the width. And the min. height of a room in the building is 2.5m
The first objective was to create a model when the height is 36m
I did it using the equation of the ellipse and my graph looks like: http://imageupload.org/pt-112919260786.html
The equation of this ellipse is y= sqrt(1296-x^2)
The QUESTION IS:
How do I find the maximum volume of the cuboid which would fit inside this curve?
The only thing I have figured is
that we know nothing about the cuboid
So I assumed the width and height to be x and 2y
So the V = 300xy (x2 as the width is 2y)
and then I plugged in the equation of the ellipse into this equation, is that the right thing to do?
But then do I differentiate?? to find what? x?
PLEASE PLEASE HELP!
THANK YOU SO MUCH GUYS!
Homework Statement
OK
I have a upside down looking curve structure (½ ellipse). It has the following specifications:
The building has a rectangular base 150m long and 72m wide. The max height of the structure should not exceed 75% of its width or be less than half the width. And the min. height of a room in the building is 2.5m
Homework Equations
The first objective was to create a model when the height is 36m
I did it using the equation of the ellipse and my graph looks like: http://imageupload.org/pt-112919260786.html
The equation of this ellipse is y= sqrt(1296-x^2)
The QUESTION IS:
How do I find the maximum volume of the cuboid which would fit inside this curve?
The Attempt at a Solution
The only thing I have figured is
that we know nothing about the cuboid
So I assumed the width and height to be x and 2y
So the V = 300xy (x2 as the width is 2y)
and then I plugged in the equation of the ellipse into this equation, is that the right thing to do?
But then do I differentiate?? to find what? x?
PLEASE PLEASE HELP!
THANK YOU SO MUCH GUYS!