Question: The optimal order size is found by finding the value of order at which the probability of having less than or equal to the order

The optimal order size is found by finding the value of order at which the probability of having less than or equal to the order size is CF. This can be found as: Q = Mean Demand + Z*SD = 20000 + 0.18*5000 = 20900 -------------------(a) E(Z) = Normal Loss Function at Z of 0.18 = 0.3154 Expected Lost Sales, L(Q) = SD*E(z) = 0.3154*5000 = 1577 Expected Sales, S(Q) = Demand - L(Q) = 20000 - 1577 = 18,423 Expected Left Over Inventory, V(Q) = Q - S(Q) = 20,900 - 18,423 = 2477 ------------(a) Expected profit = S(Q)*Cu - V(Q)*Co = 18423*$12 - 2477*$9 = $1,98,783 --------- (a) Profit of publisher = Q*($12 - $1) = 20900*$11 = $2,29,900 ------------ (b) Can you please explain how you got the E(Z)?

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