You are launching a new company producing retro turntables and you decided to subcontract out the production of the speaker portion of the turntable. You have three vendors (1, 2 and 3) to supply your speakers and their price per shipment of speakers is $2250, $2270 and $2230 respectively. (A shipment is 1,000 speakers). In addition to that you have to pay shipping costs. The shipments would go to one of your two warehouses and from there you will ship them two your two factories (1 & 2) for assembly. The costs are shown below.
Each vendor is able to supply up to 10 shipments per month but only 6 shipments to each warehouse at most. Each warehouse is able to send up to 6 shipments per month to each factory. Factory 1 requires 10 shipments per month and factory 2 requires six shipments per month.

 

Vendor 1 Vendor 2 Vendor 3 Warehouse 1 Warehouse 2 Cost per shipment $300 + $0.40 per mile $200 + $0.50 per mile $500 + $0.20 per mile Warehouse 1 1600 500 Mileage ($) 2000 Warehouse 2 400 600 1000 Shipment Cost ($) Factory 1 200 400 Factory 2 700 500 a) (10 points) Draw this network problem and write the mathematical model to determine the minimum cost necessary to meet the demand. b) (10 points) Solve using any applicable method.