I just need my solution to be put into a proper formal business letter. All you need to do is to make it look more professional.

Volume (V) = 225,000 cubic feet Foundation Cost = $ 30 per SF Sides cost = $ 20 per SF Roofing cost = $ 15 per SF Dorm is in the shape of semi circular section. Assume the base width as W and length = L Volume (V) = ( wz x-) x L = 225,000 & WIL= 225,000 x 4 x 2 3.141593 = 572,958 Foundation cost = 30 x W x L Both Sides cost = (4 w2 x;) x 2 x 20 = 15.71 W2 Roofing cost = ( x W x -) XL x15 = 23.56 WL Hence Total Cost, C = 30WL + 15.71W2 + 23.56WL = 15.71W/2 + 53.56WL 572,958 But L = W2 Hence, C = 15.71W2 + 53.56W x- 572,958 30,687,630 W2 -= 15.71W2+ W For minimum cost, first derivative of C must be zero. Hence, &C 6 (15.71W/2 + 30,687,630) = 0 W (2 x 15.71W/) + 30,687,630 x . -1 WE=0 & 31.42W/3 - 30,687,630 = 0 (30,687,630) 1/3 : W = 31.42 = 99.22 ft Length of dorn, 572,958 572958 L= W2 (99.22)2 = 58.20 ft Step 2: Dimensions of dorm with Roofing cost @ $ R per SF: Roofing cost = (n xW x-) XLXR = 1.57 WLR Hence Total Cost, C = 30WL + 15.71W2 + 1.57 WLR 572,958 But L = W2 Hence, C = 15.71W2 + 30W x 572,958 572,958 W2 + 1.57 WR X W2= 15.71W2+ 17,188,740 899,544R + W W For minimum cost, first derivative of C must be zero. Hence, SC = 0 SW 15.71W2 + 17,188,740 899,544R SW + W = 0 W : (2 x 15.71W) + 17,188,740 x + 899,544RX W2 = 0 :. 31.42W3 - 17,188,740 - 899,544R = 0 17,188,740 + 899,544R) 1/3 : W = 31.42 = (547,064 + 28, 630R) 1/3 ft Length of dorn, 572,958 572, 958 L = W2 (547, 064+ 28, 630R) 2/3 ftDear Calculus Students: After months of diligent work, I nally earned a promotion to Vice President for Development here at Dust-Mite U, which shocked quite a few. 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 resourcell 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 details). As a tting tribute to the dearly departed, the donor has designated that the Jnds be used to build a dorm in the shape of an airplane hangar, as shown 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 plane. 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 roong costs $15 per square. I need your expert advice on what the dimensions of the building should be to minimize the total cost. While the cost of the ooring and siding has been fairly stable, a further complicating factor is that the cost of roong material has been uctuating dramatically for as long as I can remember (at least two months). In addition to your recommendation for the price of $15 per square foot, I also need a recommendation on the dimensions of the dorm if the roofing costs 3R per square foot. We are meeting with the architects to discuss plans before Thanksgiving, so I would appreciate your report by November 6