Please see the attachment, thank you! Cheers! ### Problem 6.5: Boombox Speaker Supply Chain Optimization**Background:**The Audiofile Company manufactures boomboxes and requires subcontracted speakers from three potential vendors. Each vendor provides shipment pricing based on batches of 1,000 speakers.#### Vendor Pricing:| Vendor | Price ||--------|--------|| 1 | $22,500|| 2 | $22,700|| 3 | $22,300|**Shipping Details:**Shipment destinations include two designated company warehouses. Shipping charges are determined by vendor-specific formulas tied to warehouse mileage.#### Shipping Costs: - **Vendor Charge per Shipment:** | Vendor | Charge Formula | Warehouse 1 Mileage | Warehouse 2 Mileage | |--------|--------------------------|---------------------|---------------------| | 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 |**Factory Shipping Needs:**Shipments are required monthly for assembly at two factories. Costs per shipment from warehouses are detailed below, alongside the number of shipments:#### Unit Shipping Costs:| From | To Factory 1 | To Factory 2 ||------------|--------------|--------------|| Warehouse 1| $200 | $700 || Warehouse 2| $400 | $500 |- **Monthly Demand:** | Factory | Shipments Needed | |---------|------------------| | 1 | 10 | | 2 | 6 |**Constraints and Objectives:**- Each vendor can supply a maximum of 10 shipments per month.- Each vendor can send up to six shipments monthly to any single warehouse.- Each warehouse can dispatch up to six shipments per month to each factory.**Optimization Goal:**Develop a monthly plan to determine optimal shipment allocations. The strategy should minimize overall purchase and shipping costs by efficiently distributing the shipments from vendors to warehouses and onward to factories.**Network Model:**Create a network model reflecting these constraints with nodes for vendors, warehouses, and factories. This problem is akin to a minimum-cost flow problem, adjusted to

Company AF produces the speakers. The production of the speaker has been subcontracted to three…

6.5. 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 Page 232 each shipment of 1,000 speakers is shown below. Vendor Price 1 $22,500 22700 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 based on the mileage to the warehouse. These formulas and the mileage data are shown below. Vendor Charge per Shipment Warehouse 1 Warehouse 2 $300 + 40e/mile 1,600 miles 400 miles $200 + 50c/mile 500 miles 600 miles $500 + 20c/mile 2,000 miles 1,000 miles Whenever one of the company's two factories needs a shipment of speakers to assemble into the boomboxes, the company hires a trucker to bring the shipment in from one of the warehouses. The cost per shipment is given next, along with the number 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 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. unply petwo 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. However, 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 ni buuhin de lamand nada đt denieted in Fieun 610 e diseleu hes