=6.4. The Audiofile Company produces boomboxes. However, 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 warehouses. In addition to the price for each shipment, each vendor would charge a shipping cost for which it has its own formula 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 vendor, 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 purchase costs (including the shipping charge) and the shipping costs from the warehouses to the factories.