Foster Generators operates plants in Cleveland, Ohio; Bedford, Indiana; and York, Pennsylvania. Production capacities over the next three$-$month planning period for one particular type of generator are as follows:

Origin Plant Three Months Production Capacity$($Units$)$

$1$ Cleveland $5000$

$2$ Bedford $6000$

$3$ York $2500$

Total $13,500$

Management would like to determine how much of its production should be shipped from each plant to each distribution center. The objective is to determine the routes to be used and the quantity to be shipped via each route that will provide the minimum total transportation cost. The cost for each unit shipped on each route is given in the following table:

Complete the model formulation $($objective function and constraints$).$ Solve the model using Excel Solver.