A method for controlling an electro-mechanical transmission operatively coupled to first and second electric machines (56,72) to transmit power to an output member, the method comprising: determining motor torque constraints for the first and second electric machines (56,72); determining battery power constraints for an electrical energy storage device electrically connected to the first and second electric machines (56,72); determining a range for a first torque input to the electro-mechanical transmission; determining a range for a second torque input to the electro-mechanical transmission; and determining a preferred output torque to the output member of the electro-mechanical transmission that is achievable within the motor torque constraints, is achievable within the range for the first torque input, is achievable within the range for the second torque input, and is based upon the battery power constraints, characterized in that the method further comprises: formulating mathematical equations representing maximum and minimum motor torque constraints for the first and second electric machines (56,72) and representing maximum and minimum battery power constraints; formulating a mathematical equation representing the output torque; formulating mathematical equations representing the range for the first torque input; formulating mathematical equations representing the range for the second torque input; transforming the mathematical equations representing the maximum and minimum battery power constraints to equations of concentric circles having respective radii; transforming the mathematical equations representing the maximum and minimum motor torque constraints for the first and second electric machines to equations consisting of lines; transforming the mathematical equations representing the range for the first torque input to equations consisting of lines; transforming the mathematical equations representing the range for the second torque input to equations consisting of lines; and transforming the mathematical equation representing the output torque to an equation consisting of a line. determining motor torque constraints for the first and second electric machines (56,72); determining battery power constraints for an electrical energy storage device electrically connected to the first and second electric machines (56,72); determining a range for a first torque input to the electro-mechanical transmission; determining a range for a second torque input to the electro-mechanical transmission; and determining a preferred output torque to the output member of the electro-mechanical transmission that is achievable within the motor torque constraints, is achievable within the range for the first torque input, is achievable within the range for the second torque input, and is based upon the battery power constraints, characterized in that the method further comprises: formulating mathematical equations representing maximum and minimum motor torque constraints for the first and second electric machines (56,72) and representing maximum and minimum battery power constraints; formulating a mathematical equation representing the output torque; formulating mathematical equations representing the range for the first torque input; formulating mathematical equations representing the range for the second torque input; transforming the mathematical equations representing the maximum and minimum battery power constraints to equations of concentric circles having respective radii; transforming the mathematical equations representing the maximum and minimum motor torque constraints for the first and second electric machines to equations consisting of lines; transforming the mathematical equations representing the range for the first torque input to equations consisting of lines; transforming the mathematical equations representing the range for the second torque input to equations consisting of lines; and transforming the mathematical equation representing the output torque to an equation consisting of a line. formulating mathematical equations representing maximum and minimum motor torque constraints for the first and second electric machines (56,72) and representing maximum and minimum battery power constraints; formulating a mathematical equation representing the output torque; formulating mathematical equations representing the range for the first torque input; formulating mathematical equations representing the range for the second torque input; transforming the mathematical equations representing the maximum and minimum battery power constraints to equations of concentric circles having respective radii; transforming the mathematical equations representing the maximum and minimum motor torque constraints for the first and second electric machines to equations consisting of lines; transforming the mathematical equations representing the range for the first torque input to equations consisting of lines; transforming the mathematical equations representing the range for the second torque input to equations consisting of lines; and transforming the mathematical equation representing the output torque to an equation consisting of a line.