Consider a serial supply chain system with five installations (stages) that have the setup and unit holding costs shown in the table below. The demand rate is d = 1,000 units / week. K; ($/order) h ($/unit/week) Installation (i) 125,000 20,000 10 6,000 10,000 3 15 4 20 5 250 30 We would like to find an optimal or near optimal inventory policy with inventory coordination from one stage to the next. For this purpose, answer the following questions: (a) If possible, consolidate some of the stages of the supply chain. After that, solve the relaxed problem and generate a lower bound to the cost of the optimal policy. Provide the order quantities and the corresponding cost per time unit (lower bound). (b)lf possible, use the exact method to find the optimal inventory policy. If the exact method cannot be applied, use Roundy's 98% approximation method. Provide the order quantities and corresponding cost for the original problem (with 5 stages). (c) Verify that the solution in part (b) is within 2% of the lower bound.