[critical fractile problem] To minimize your average cost per year, how many canisters should you send on the annual supply ship?

Q2: Supplying a Remote Outpost Your firm operates a remote mining outpost in coastal Alaska. The outpost is supplied once per year by ship and more frequently by aircraft. Over the 20 years the outpost has been in operation, the number of canisters of de-icing fluid the outpost uses per year has followed the distribution below: Canisters Probability 5% 5% 10% 20% 25% 20% 10% 5% 0 4 The canisters cost $40 each to purchase from the manufacturer. There are two ways to send the canisters to the outpost: first, they may be put on the annual supply ship at a transportation cost of S15 each. If the outpost runs out of canisters before the next supply ship arrives, more may be sent in by air at a transportation cost of $50 each. At the end of the year, all canisters at the outpost must be shipped back, whether they have been used or not, because they only have a limited shelf life. The return transportation is by the retum voyage of the annual supply ship and costs $15 per canister, whether the canister has been used or not. Unused canisters, even if they are at the end of their shelf life, are accepted back by the manufacturer for a $20 credit each