Following the snowstorm of 2014 in the Atlanta Metro Area, the State of Georgia
ID: 2857092 • Letter: F
Question
Following the snowstorm of 2014 in the Atlanta Metro Area, the State of Georgia has taken several steps to prepare for an event of similar magnitude and impact in the future. Assume that the State has contracted with a manufacturer in the Midwest specializing in storage facilities to design special alloy tanks. These tanks hold sand and salt to de-ice roads and keep the highways open to traffic in periods of bad weather. The manufacturer has been told that the storage facilities must be cylindrical, and each must hold a volume of 400 m^3. The base material costs $75/m^2 and the material used for the sides costs $50/m^2. Assume that the State has budgeted half a million dollars to acquire these storage facilities to expand their existing storage capacity and would like to obtain the maximum number of facilities possible. Assuming that the lids will be provided by another vendor, what design dimensions will minimize the total costs of each bin? How many facilities can be built with the available budget? Because of an unforeseen shortage of materials, the cost of the material used for the sides suddenly increases by 5%. What happens to the following: (a) Optimum dimensions; Optimum cost of each facility, and (c) number of reservoirs that can be purchased w ith the available budget?Explanation / Answer
volume should be equal to 400 = pi r^2*h
=> h = 400/pir^2
cost = pi *r^2 *75+ 2pi rh *50
so cost = 75 pi r^2 +100 pi * r * 400 /pi r^2
cost = 75 pi r^2 +40000 /r
d/dr(cost ) = 150 pi r -40000/r^2 = 0
r^3 = 40000/150 pi => r= 9.427 m
so h = 400/(pi*9.427^2) = 1.4327 m -----design dimensions ( r= 9.427 and h = 1.4327)
so cost for each bin = pi *9.427^2*75+ 100*pi *9.427*1.4327 =$25182.2
so no of bins = 500000/25182.2 =19.855 => 19 complete bins
c) cost increased by 5% => 1.05*50 = 52.5 . repeat the same calcualtions shown above to obtain answer . do it as practice for you because the steps are same as shown above