Problem 1 (45 points): This problem is a combination of binary integer programming and transportation problem The Audiofile company produced 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 and supply capacity is shown below. Each shipment would go to one of the Audiofile company's four factories. In addition to the price for each shipment, each vendor would charge a shipping cost. There are two types of costs associated with the shipping: set-up costs (fixed costs) of shipping and transportation costs which depend on the distance. Each vendor has its own formula based on the mileage to the factory. The fixed sipping cost, three formulas, and the mileage data are shown below. Certain shipping routes that are impossible are marked with the infinity symbol (). Considering that the demand of a factory needs to be satisfied and a factory may be delivered to from several vendors. a. Formulate algebraically the corresponding model that will determine which vendors should be purchased from to fulfill the objective which is to minimize the sum of the purchase costs and the shipping costs, while satisfying all demands. Define the decision variables, objective function, and constraints. (25 points) Problem 1 (45 points): This problem is a combination of binary integer programming and transportation problem The Audiofile company produced 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 and supply capacity is shown below. Each shipment would go to one of the Audiofile company's four factories. In addition to the price for each shipment, each vendor would charge a shipping cost. There are two types of costs associated with the shipping: set-up costs (fixed costs) of shipping and transportation costs which depend on the distance. Each vendor has its own formula based on the mileage to the factory. The fixed sipping cost, three formulas, and the mileage data are shown below. Certain shipping routes that are impossible are marked with the infinity symbol (). Considering that the demand of a factory needs to be satisfied and a factory may be delivered to from several vendors. a. Formulate algebraically the corresponding model that will determine which vendors should be purchased from to fulfill the objective which is to minimize the sum of the purchase costs and the shipping costs, while satisfying all demands. Define the decision variables, objective function, and constraints. (25 points)