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v2 will either be sold or remain unsold. If p represents the probability of selling one additional unit, then (1-p) must be the probability of not selling it. If the additional unit is sold, the conditional profit will increase as a result of the profit earned from this unit. This is termed as incremental (marginal) profit. IP. If the additional unit is not sold, the conditional profit reduces and the amount of reduction is called the incremental (marginal) loss, IL resulting from stocking of an item that is not sold Additional units should be stocked so long as the expected incremental profit from stocking each of them is more than the expected incremental loss from stocking each. The expected incremental profit from stocking and selling an additional unit is the incremental profit of the unit multiplied by the probability that the unit would be sold i.e.,p(IP). The expected incremental loss from stocking and not selling an additional unit is the incremental loss incurred if the unit remains unsold multiplied by the probability that the unit would not be sold i.e., (1-P)(IL). Thus the units should be stocked upto the point where p(IP) = (1 - p) (IL) IL p(IP + IL) = IL or p = IP + IL The letter p represents the minimum required probability of selling at least an additional unit to justify the stocking of that additional unit. Additional units should be stocked so long as the probability of selling at least an additional unit is greater than p. EXAMPLE 9.5-5 A milkman buys milk at 12 per litre and sells for 15 per litre. Unsold milk has to be thrown away. The daily demand has the following probability distribution: Demand (litres) 46 48 50 52 54 56 58 60 62 64 Probability 0.01 0.03 0.06 0.10 0.20 0.25 0.15 0.10 0.05 0.05 If each day's demand is independent of previous day's demand, how many litres should be ordered every day? [Rajasthan M.B.A., 1982]