Consider a representative firm with the following production function: = (. ) = ()1, where 0 < < 1. As we learned in class, the representative firm maximizes its profits given by = .Suppose that = 30, = 1, and = 1. Solve the maximization problem of the firm. What are the optimal 3 level of hours hired (assuming that the unit of is an hour), output, and profits of the firm as functions of wage ? (6 points) (Hint: =(1)(),andtheoptimalityconditionis =.)