In the formal presentation of the Newsvendor problem, we have shown that the profit maximization problem is equivalent to the minimizing of the following cost function:

C(Q) = E[Cu (D Q)+ + Co (Q D)-] or,

C(Q) = CuE[short] + CoE[left]

Assume that the demand is normally distributed with mean and standard deviation . By using the characterization (i.e., expression) for the optimal order quantity, Q*, show that the optimal cost can be expressed as C(Q ) = A(Cu, Co) , where A(Cu, Co) is a constant which is a function of the cost parameters C and C but not of the parameters (, ) of the demand distribution D. What can you infer for the maximum profit that the newsvendor can gain by ordering the optimal quantity?