Post Utme Nile University 2020 Economics Question 33

Consider a firm that produces two goods, A and B. The production function for good A is given by \( Q_A = 2L_A + 3K_A \), where \( Q_A \) is the quantity of good A, \( L_A \) is the labor used in producing good A, and \( K_A \) is the capital used in producing good A. The production function for good B is given by \( Q_B = 3L_B + 2K_B \), where \( Q_B \) is the quantity of good B, \( L_B \) is the labor used in producing good B, and \( K_B \) is the capital used in producing good B. If the firm has 10 units of labor and 5 units of capital, find the optimal allocation of labor and capital between the two goods.