The owner of a generating unit would like to maximize its profit by selling both energy and balancing services. Write the objective function and the constraints for this optimization problem. Discuss the various cases that might arise depending on the price paid for energy and balancing. Neglect the constraint introduced by the ramp rate of the generating unit. (Hint: Equation (5.14) of Example 5.6 must be modified because providing balancing services might involve a reduction in the output of the generating unit. On the other hand, you may need to consider explicitly that the amount of balancing service sold must be positive, that is x2 ≥ 0.)