Expected Profit from an Order

Assume demand to be normally distributed, with a mean /n and standard deviation a. Each unit sells for a price p and costs c. Any unsold units fetch a salvage value of s. Obtain an expression for the expected profit if O units are ordered. 

If 0 units are ordered and demand turns out to be x O, each of the x units sold contributes p - c, whereas each of the O - x) units unsold results in a loss of c - s. If demand is larger than 0, each of the O units sold contributes p — c. We thus obtain 

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