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6.5. The Audiofile Company produces boomboxes. How- ever, management has decided to subcontract out the production of the speakers needed for the boomboxes. Three vendors are available to supply the speakers. Their price for each shipment of 1,000 speakers is shown below. Vendor Price 1 $22,500 2 22,700 3 22,300 Each shipment would go to one of the company's two ware- houses. In addition to the price for each shipment, each vendor would charge a shipping cost for which it has its own formula based on the mileage to the warehouse. These formulas and the mileage data are shown below. Charge per Shipment Vendor Warehouse 1 Warehouse 2 1 $300 + 40/mile 1,600 miles 400 miles 2 $200 + 50/mile 500 miles 600 miles 3 $500 + 20/mile 2,000 miles 1,000 miles Whenever one of the company's two factories needs a ship- ment of speakers to assemble into the boomboxes, the company hires a trucker to bring the shipment in from one of the ware- houses. The cost per shipment is given next, along with the num- ber of shipments needed per month at each factory. Unit Shipping Cost Factory 1 Factory 2 Warehouse 1 $200 $700 Warehouse 2 400 500 Monthly demand 10 6 Each vendor is able to supply as many as 10 shipments per month. However, because of shipping limitations, each vendor is only able to send a maximum of six shipments per month to each warehouse. Similarly, each warehouse is only able to send a maximum of six shipments per month to each factory. Management now wants to develop a plan for each month regarding how many shipments (if any) to order from each ven- dor, how many of those shipments should go to each warehouse, and then how many shipments each warehouse should send to each factory. The objective is to minimize the sum of the pur- chase costs (including the shipping charge) and the shipping costs from the warehouses to the factories. a. Draw a network that depicts the company's supply network. Identify the supply nodes, transshipment nodes, and demand nodes in this network. b. This problem is only a variant of a minimum-cost flow problem because the supply from each vendor is a maximum of 10 rather than a fixed amount of 10. How- ever, it can be converted to a full-fledged minimum- cost flow problem by adding a dummy demand node that receives (at zero cost) all the unused supply capacity at the vendors. Formulate a network model for this minimum-cost flow problem by inserting all the necessary data into the network drawn in part a supplemented by this dummy demand node. (Use the format depicted in Figure 6.3 to display these data.) c. Formulate and solve a spreadsheet model for the company's