probabilities

Problem 2. (Inventory problem.) Suppose that the bicycle dis- tributor is offered very favourable terms on the purchase of the model under consideration, whose production is to be discounted. The unit cost of each bicycle is $20. Each bicycle can be sold, in the period 20-25 December, for $45, for a profit of $25. The problem is that the distributor does not know the exact demand. Suppose he lives in a small village and estimates the demand D to be 0, 1, or 2, equiprobably. Bicycles unsold in the mentioned period 20-25 December, will be sold later for a much cheaper price; besides they occupy some space in the storage, etc. Thus each of them gives income (not profit!) of only $7. Find the best number of bicycles, y*, to be bought by the dis- tributor (a) Use the expected value criterion. (b) Draw the decision tree and analyse it in the usual way