We conclude that the optimal wholesale price w 2 0

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We conclude that the optimal wholesale price w * 2 = 0 . 588. Here we only list the relevant values of w 2 . Finding these six values certainly requires more trials. Note that in this problem, we find the “optimal” w 2 by fixing w 1 . We may then fix w 2 and optimize over w 1 , fix w 1 and then optimize over w 2 , etc. This process is just like what we did to q 1 and q 2 . We will be able to find the equilibrium pair of wholesale prices ( w * 1 , w * 2 ) eventually. w 2 ( w 2 - c 2 ) q * 2 0.58 0.1854653 0.59 0.1855341 0.60 0.1853495 0.587 0.1855401 0.588 0.1855406 0.589 0.1855386 Table 1: Searching w 2 Day Demand IP B t IP E t Order IL B t IL E t In-transit 3 32 65 33 0 65 33 0 4 25 33 8 92 33 8 0 5 19 100 81 0 8 -11 92 6 16 81 65 0 81 65 0 7 22 65 43 0 65 43 0 8 19 43 24 76 43 24 0 9 24 100 76 0 24 0 76 10 16 76 60 0 76 60 0 Table 2: Results for Problem 3a 3. (a) The order quantities, inventory positions, inventory levels, and number of in-transit items for the remaining eight days are listed in Table 2. (b) Figure 1 depicts s (the lower black line), S (the upper black line), IP E t (the red line), and IL E t (the blue line). Whenever the inventory position drops below s , we will place an order to increase the inventory position to S . This increases the number of units in transit, which is included in inventory positions. However, in-transit items are not included in inventory levels and will become on hand one day later. That’s why the inventory level keeps going down (for only one period). 1 2 3 4 5 6 7 8 9 10 -20 0 20 40 60 80 100 120 Day Quantity (unit) Figure 1: The graph for Problem 3b 2
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