6. A company that produces heaters in four locations expects to produce 50 in Biloxi, 70 in Denver, 60 in Las Vegas, and 80 in St. Paul (all in thousands). The coils for the heaters are being produced by a company with manufacturing centers in LA, Atlanta, and Chicago. These plants are capable of producing 100, 80, and 80 coils respectively (in thousands). Because of variation in production and transportation costs, the profit per unit varies. These values are given below: LA Atlanta Chicago Biloxi 8 12 10 Denver 12 16 18 Las Vegas 8 St. Paul 12 12 10 10 16 A. Draw a network diagram with nodes representing locations and arcs connecting the nodes. Be sure to include the per-unit profits as well as supply and demand amounts. B. Let X11 represent the number of goods transported from location 1 to receiving location 1 (# of items from LA to Biloxi). Let X12 represent the number of goods transported from location 1 to receiving location 2 (# of items from LA to Denver), and so on. Given that our goal is to maximize profits while simultaneously meeting demand, set up the Objective Function. C. Now formulate the supply constraints.