BASF sells customized petrochemical catalysts that are produced in a plant in Germany. Many of their customers are in North America and transportation is done via ocean carrier. They can purchase container capacity in advance at the price of $3000 per container. However, if they advance purchase containers, they bear the risk of not knowing their exact needs for containers. In particular, here is a forecast of their needs for June (i.e., a density and distribution function): Q f(q) 0 0.1810 F(Q) 0.0952 Q f(q) F(Q) 11 0.0.201 0.8997 1 0.1482 0.2592 12 0.0164 0.9179 2 Q.1213 0.3935 13 0.0134 0.9328 3 0.0993 0.5034 14 0.0110 0.9450 4 0.0813 0.5934 15 0.0090 0.9550 5 0.0666 8.6671 16 0.0074 0.9631 6 0.0545 0.7275 17 0.0060 0.9698 7 0.0446 0.7769 18 0.0049 0.9753 8 0.0365 0.8173 19 0.0040 0.9798 9 0.0299 0.85.04 20 0.0033 0.9834 10 0.0245 0.8775 If they purchase a container in advance and don't actually need it, then they will fill it with some excess "filler" product and store it in North America until it can be sold. The expected extra storage cost is $750 per container. For example, if their needs are for 2 containers but they advanced purchased 3 containers, then they ship all three containers and incur an extra $750 charge for the 1 container filled with "filler" product. Containers purchased on the spot market (after they learn their needs) are expected to cost $5000 per container. For example, they may advance purchase 1 container but discover that they need 3 containers, in which case they would purchase an additional 2 containers at $5000 each. How many containers should they advance purchase to minimize their costs? Report your answer as an integer.