BG is a technology company that wants to open a new warehouse for new product A. Forecasts show that at a given time the probability of needing Y number of storage units for product A is given by the following function: F(Y)= min (1,(Y/1000)^0.25). There are three alternative warehouse designs with following cost structures.

-Compact: Cc(x) = 100+x

-Medium : Cm(x) = 300+ x/2

-Large: Cl(x) = 520 +x/4

Let k E (0,1) be the maximum probability for storage unit shortages that BG can tolerate. What is the minimum cost of building a warehouse for k=0.05?