# Math Help - Optimization problem

1. ## Optimization problem

a Donor is willing to build a new hangar for the program with the following stipulations
- the hangar must be in the shape of a half cylinder
- the hangar to have an exact volume of 225000 cubit feet
We would like to minimize the cost of the building. Currently, the construction costs for the foundation are $30 per square foot, the sides cost$20 per square foot to construct, and the roofing costs $15 per square foot. what should the dimensions of the building be to minimize the total cost ? 2. Originally Posted by genie2010 a Donor is willing to build a new hangar for the program with the following stipulations - the hangar must be in the shape of a half cylinder - the hangar to have an exact volume of 225000 cubit feet We would like to minimize the cost of the building. Currently, the construction costs for the foundation are$30 per square foot, the sides cost $20 per square foot to construct, and the roofing costs$15 per square foot. what should the dimensions of the building be to minimize the total cost ?
- the hangar must be in the shape of a half cylinder ... $V = \frac{\pi}{2}r^2 h$

- the hangar to have an exact volume of 225000 cubic feet ... $225000 = \frac{\pi}{2}r^2 h$

foundation area ... $F = 2rh$

roof area ... $R = \pi r h$

"sides" (actually, the vertical ends) area = $\pi r^2$

set up a cost function, get the cost function in terms of a single variable ( $r$ or $h$, whichever is easier), and find the value of that variable that minimizes the cost using the techniques taught to you in class.