I minimizing the cost of this building? immediate help

[geekysayra]

i need help minimizing the cost of this building? immediate help pleasez

A university has decided to build a new, creative dorm! After a contest to determine the shape, it was decided that the dorm would be in the shape of an airplane hangar that has semicircular ends. There is an additional stipulation: the volume of the dorm must be exactly 225,000 cubic feet.

the dorm is going to look like a cylinder cut vertically in half. the height is y the width is x and the radius is x

Part 1
The university is in the planning stages with the architects now, and they would obviously like to minimize the cost of the building. This is where the university needs your help. Currently, the construction costs for the foundation are $30 per square foot, the sides (the two ends) cost $20 per square foot to construct, and the roofing cost $15 per square. The university needs your expert advice on what the dimensions of the building should be to minimize the total cost.

Determine the optimal dimensions and and the minimized cost, under these conditions


ps. there is an attachment that shows what the dorm will look like and its dimensions

 

[tiny-tim]

Welcome to PF!

Hi geekysayra! Welcome to PF!

What equation have you got for the cost of any particular design?

 

[geekysayra]

well the that's the problem i wasn't given an equation, that was all i was given. that really sucks, i don't somebody is going to be able to help me because i can't even help myself lol

 

[tiny-tim]

well the that's the problem i wasn't given an equation, that was all i was given. that really sucks, i don't somebody is going to be able to help me because i can't even help myself lol

Just make an equation from this:

the construction costs for the foundation are $30 per square foot, the sides (the two ends) cost $20 per square foot to construct, and the roofing cost $15 per square