I would like to know all the steps to minimize total cost and what the dimensions for that what be. And then for the second part what the dimensions of dorm would be of roofing cost $R per square foot. I would need to use calculus optimization rules for this assignment. I would appreciate if all steps were demonstrated especially for the second part, thank you.

After months of diligent work, I finally earned a Promotion to Vice President for Development here at Dust-Mite U. I'm very proud of my fund-raising accomplishments, but sometimes the gifts come with very strict limitations on how they can be used. We just received such a donation, and when I went looking for help, your enterprising and resourceful professor naturally referred me to you. We have a somewhat eccentric alum who has made a major contribution in memory of his favorite Chia Pet, Airplane, that recently passed away in a bizarre gardening accident (it's best we not discuss the de- tails). As a fitting tribute to the dearly departed, the donor has designated that the funds be used to build a dorm in the shape of an airplane hanger, a half cylinder like the one seen below. There is an additional stipulation on the gift: the volume of the dorm must be exactly 225,000 cubic feet, which is one cubic foot for each sprout on the Chia Pet. We're in the planning stages with the architects now, and we would obviously like to minimize the cost of the building. This is where I need your help. 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. I need your expert advice on what the dimensions of the building should be to minimize the total cost. While the cost of the flooring and siding has been fairly stable, a further complicating factor is that the cost of roofing material has been fluctuating dramatically for as long as I can remember (at least two months) I also need a recommendation on the dimensions of the dorm if the roofing cost $R per square foot, so we can use the recommendation as prices change