Suppose a company has a monopoly on a game called Monopoly and faces a demand curve given by QT = 100??P and a marginal revenue function given by MR = 100 2QT where QT equals the combined total number of games produced per hour in the company's two factories (QT = q1 + q2). If factory 1 has a marginal cost function given by MC1 = q1  5 and factory 2 has a marginal cost function given by MC2 = 0:5q2 ?? 5, how much total output will the company choose to produce and how will it distribute this production between its two factories in order to maximize profits?