Suppose that instead of measuring shortage in terms of cost per shortage per year, a cost of P dollars is incurred for each unit the firm is short. This cost does not depend on the length of time before the backlogged demand is satisfied. Determine a new expression for the annual shortage cost as a function of Q and

b, and solve GMB’s problem (Example 12.3) with this way of costing shortages for reasonable values of P. (What values of P do you think are reasonable?)