Suppose that instead of measuring shortage in terms of cost per shortage year, a cost of S 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 TC(q, M), and explain how to determine optimal values q* and M*.
4 For the model developed in this section, determine
a the average length of time it takes to meet demand for a unit.
b the fraction of all demanded units that are back- ordered.