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A building is the shape of an airplane hanger (a half cylinder). Construction for the foundation (rectangular part) costs $30 per square foot, the sides (semicircle bases) cost $20 per square foot and the roofing cost $15 per square foot. The volume of the entire building is 225,000 cubic feet. What should the dimensions of the building be to minimize the cost?
For my answer I got:
radius: 49.6117
height (in this case length): 58.1962
Could someone confirm my answers? Thank you very much.
2 answers
How did you get those answers?
For a fixed volume, radius is a function of length.
(1/2) pi r^2 L = 225,000
L (r) = 450,000/(pi r^2)
Cost = L*2r*30 + pi*r^2*20 + pi*r*L*15
Write cost as a function of one variable and set the derivative equal to zero. Then solve for the unknown dimension.
If that is what you did, and no mistakes were made, than your answers are correct
For a fixed volume, radius is a function of length.
(1/2) pi r^2 L = 225,000
L (r) = 450,000/(pi r^2)
Cost = L*2r*30 + pi*r^2*20 + pi*r*L*15
Write cost as a function of one variable and set the derivative equal to zero. Then solve for the unknown dimension.
If that is what you did, and no mistakes were made, than your answers are correct
9 answers