Please provide a mathematical (algebraic) formulation for each problem along with a solution using the Excel Solver.

The mathematical formulation should clearly provide notation and a descriptive statement for decision variables, objective function, and constraints.

The Bavarian Motor Company (BMC) manufactures expensive luxury cars in Hamburg, Germany, and exports cars to sell in the United States. The exported cars are shipped from Hamburg to ports in Newark, NJ and Jacksonville, FL. From these ports the cars are transported by rail or truck to distributors located in Boston, MA, Columbus, OH, Atlanta, GA, Richmond, VA, and Mobile, AL. The figure below shows the possible shipping routes available to the company along with the transportation cost for shipping each car along the indicated path. Each location is termed as a node and numbered for convenience in defining decision variables.

Note that Newark and Jacksonville are supply nodes (only supplies). Richmond is a demand node (can only receive). Boston, Columbus, Atlanta, and Mobile are transshipment nodes (can both receive and supply while ensuring their requirements). Currently, 200 cars are available at the port in Newark and 300 are available in Jacksonville. The number of cars needed by the distributors in Boston, Columbus, Atlanta, Richmond, and Mobile are 100, 60, 170, 80, and 70, respectively. BMC would like to determine the least costly way of transporting cars from the ports in Newark and Jacksonville to the cities where they are needed.

$30 Boston $50 Newark Columbus $40 $40 $30 Richmond $35 Atlanta $50 $25 $45 35 Jacksonville Mobile $50