Question

I have a solution, but don't know how to get it:

3. A businessman purchases perishable commodities in the wholesale market at $10 each and sells them on the retail market at $15 each. He hence makes a profit of $5 for every unit he sells. But the commodities are perishable and so any units unsold at the end of the day are discarded and he incurs a loss of $10 on each unit he discards. (I've chosen toy numbers just to keep the arithmetic simple; the important thing is the principle behind the problem.) Long experience has taught the businessman that his daily demand D has a binomial distribution with parameters n 5 and p 2/3. In other words, his demand on a given day satisfies D. The businessman has to purchase the commodities ahead of the daily demand though he does not know exactly what the demand will be. How many items should he purchase so as to maximise his expected profit? iOr, for all you budding entreprencurs, on the importance of a principled take on inventory. SOLUTION: Optimal size of inventory c 3 resulting in the largest expected profit of $11.11 Looking back at the problem, this is certainly intuitive. If our intrepid businessman pur chases too few commodities then he loses a profit opportunity in the excess demand that he does not satisfy; if he purchases too many commodities then he incurs a loss because he has to discard a lot of them. So c should the profit is not excessively large âÄT in which case we would gamble more aÄT or very small âÄt in which case we would be very conservative). But we know for the binomial that the expected demand is 5 x 2/33.33. I is satisfying that this is exactly where our calculations land us. But we should not let our little success run to our heads: intuition has its limits. Redo the problem when the profit per item is large and when it is small to see what happens. Are the limits when the profit per item go to oo and 0, respectively. intuitive? be somewhere near the expected demand Gif

Answer 1

np JF K - be denate sells. every umithe 0 makimise his expeotd Poofit e3 333 3.233 e (t) 33 expectてch P70