# Math Help - Optimizing minimal cost

1. ## Optimizing minimal cost

This problem is on optimizaton.
An airplane hanger (looks like a right circular cylinder cut in half long ways) must have a volume of exactly 225,000 cubic feet. Want to minimize cost of building it when the foundation cost $30 per square foot, siding cost$20 per sq ft, and roofing cost $15 per sq ft. What are the dimensions of the hangar to achieve minimal cost???? Also, roofing costs fluctuate so what are the dimensions of the hangar if the cost of roofing is$R per sq ft?

2. Dear zackmo11,

1st step: declare the cost function:
cost = area_found*rate_found + surface_side*rate_side+surface_proof*rate_proof.

2nd step: let r and h the radius and the height of the semi-cylinder.Express the area_found and the 2 kind of surface with r and h

3th step: Look for a connection between h and r. We have to remark that r and h is not independent because volumen V is fix --> V(r, h) = const.

4th step: express the cost function with only one variant (r or h). So we get cost(r) function.

5th step: look for the minimum