Construct a mathematical model in the form of a linear programming problem.  Then solve the problem by the simplex, dual problem, or big M methods.

A company produces motors for washing machines at factory A and factory B. The motors are then shipped to either plant X or plant Y, where the washing machines are assembled. The maximum number of motors that can be produced at each factory monthly, the minimum number required monthly for each plant to meet anticipated demand, and the shipping charges for one motor are given in the table. Determine a shipping schedule that will minimize the cost of transporting the motors from the factories to the assembly plants.