A Factory Produces Product a According to the Production Function

Multiple Choice

A factory produces product A according to the production function Q_A = 100X_A, where X_A denotes the amount of input and Q_A is the quantity produced. It also produces product B according to the production function Q_B = 200X_B - X_B², where X_B denotes the amount of input and Q_B is the quantity produced. The total available amount of input X is 100 units. The firm's profit-maximizing allocation of input X is:

A) X_A = 60 and X_B = 40.
B) X_A = 50 and X_B = 50.
C) X_A = 0 and X_B = 100.
D) X_A = 100 and X_B = 0.
E) X_A = 30 and X_B = 70.