min √(x) s.t. μ 20 with variable μ Rm. In particular, show that an optimal solution μ* to this program must satisfy T n t=1 j=1 T n P(Rt(*)¹Ã¡) Ai‚j ≤ xi, Vi, ΣΣP (Rt‚j ≥ (µ*)'Aj) (µ*)¹A; = (µ*)¹x. t=1 j=1 (1) (2)

At the beginning of each week, a machine is in one of four conditions: 1 = excellent; 2 = good; 3 = average; 4 = bad. The weekly revenue earned by a machine in state 1, 2, 3, or 4 is 100, 90, 50, or 10, respectively. After observing the condition of the machine at the beginning of the week, the company has the option, for a cost of 200, of instantaneously replacing the machine with an excellent machine. The quality of the machine deteriorates over time, as shown in the file P10 41.xlsx. Four maintenance policies are under consideration: Policy 1: Never replace a machine. Policy 2: Immediately replace a bad machine. Policy 3: Immediately replace a bad or average machine. Policy 4: Immediately replace a bad, average, or good machine. Simulate each of these policies for 50 weeks (using at least 250 iterations each) to determine the policy that maximizes expected weekly profit. Assume that the machine at the beginning of week 1 is excellent.

Explain the McKinsey 7-S model.