3. James has a monopoly on a board game called "Fly High" and faces a demand curve given by \( Q_T = 100 - P \), where \( Q_T \) equals the combined total number of games produced per hour in the company's two factories (\( Q_T = q_1 + q_2 \)). If factory 1 has a marginal cost function given by \( MC_1 = q_1 - 5 \) and factory 2 has a marginal cost function given by \( MC_2 = 0.5q_2 - 5 \), how much total output will James choose to produce and how will he divide this output between its two factories in order to maximize profits? (10%)