Jefferson Distributing is analyzing distribution networks with either 4, 5, 6 or 7 warehouses to serve 200 major customers in Europe. Relevant costs include transportation cost from the warehouses to customers, fixed facility costs, and inventory costs in the warehouses. The table below shows the annual transportation cost produced by a facility location software tool for locating 4, 5, 6 or 7 warehouses for this company. Suppose that annual inventory cost for the network can be modeled as $800,000 times the square root of the number of warehouses. Thus, if the network has 4 warehouses, then the annual inventory cost would be $800,000*4 = $1,600,000.

Number of Warehouses	Transportation Cost
4	8,000,000
5	6,500,000
6	5,000,000
7	4,400,000

a) If the annual fixed cost per warehouse is $1,000,000, how many warehouses should there be to minimize the total (transportation + warehouse + inventory) cost?

b) Now suppose the annual fixed warehouse cost is not known, but it is the same for 4, 5, 6 or 7 warehouses. What range of values for the fixed warehouse cost (in dollars per year) would ensure that four warehouses provides the lowest total (transportation + warehouse + inventory) cost?