Given the solution u* to problem (5.3.3), define the subset A: (j.A : u; ~ u;+Il. Prove that u*

00 is the unique solution to problem (5.3.3[A:]). (Use a direct argument by contradiction. Assmning the contrary, construct a feasible solution to (5.3.3) having lower cost than u*.) 5.8 To construct a policy according to Section 5.3.6 entails minimizing the function C+(u) over the interval [I, 2). The text outlines the approach in general terms. This problem fills in the details.

The proof ofTheorem 5.3.7 (Section 5.3.8) shows how to compute the breakpoints, denoted x(m), and provides a fonnula for 11 -j-(m) as a function ofg. Using this infonnation, and notation of your invention, write an explicit expression for C+(u). The expression should clearly look like the cost function of an EOQ model over each of several subintervals. (For simplicity, assume the x(m) are all distinct and strictly larger than I.) Explain how to optimize C+ (g) over each subinterval.