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a 6.8 Allocating Components to Assemblies: Biking.com is a web-based company that sells bicycles on the Internet. Its distinctive feature is that it allows cus- tomers to customize the design when they order and then to receive quick delivery. Biking.com gives customers choices for frame size (34, 36, 38), suspension (standard or heavy-duty), and gear speeds (5, 10, 15). As a result , customers can order one of 18 possible combinations (3x2x3). The company shorthand refers to frame size as Option A (A1 is the 34-in. model, A2 is the 36-in. model, and A3 is the 38-in. model). Similarly, the standard suspension is option B1, and the heavy-duty suspension is B2. The gear speeds are C1 (5), C2 (10), and C3 (15). Rather than stock 18 different types of bicycles, the company holds inventories of the major components and then assembles the bikes once a customer order comes in. Orders are taken Mondays through Wednesdays, assemblies are done on Thursdays, and shipments go out on Fridays. Thus, at the close of business on Wednesday, the company has an inventory of components and a list of orders, and its task is to match compo- nents with orders to meet as much demand as possible. The tables below describe customer orders for this week and the inventory status at the end of Wednesday Model 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 1 2 1 1 1 1 1 2. 2 2 B 1 1 1 2 2 2 1 1 1 1 2. 3 1 2 3 1 2 3 Orders 4 5 0 5 1 7 0 4 8 2 1 2 2 3 3 3 3 3 3 2 2 1 1 1 2 2 2 2 3 1 2 3 1 2 3 2 0 5 6 4 0 1 5 1 Component 1 A2 1 B2 ci C2 C3 Inventory 12 20 30 20 25 18 16 20 (a) What is the maximum number of customer orders that can be satisfied this week? (b) Suppose that the profitability varies by model type, as shown in the table below. What is the maximum profit that can be achieved from this week's orders? Model 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Profit 45 55 70 65 75 90 47 57 72 67 77 92 50 60 75 70 80 95