Post Utme Noun 2018 Economics Question 39

Consider a firm that produces two goods, A and B, u\sing two inputs, labor and capital. The production functions for the two goods are given by \( Q_A = 10L^0.5K^0.5 \) and \( Q_B = 20L^0.3K^0.7 \), where \( Q_A \) and \( Q_B \) are the quantities of goods A and B, respectively, and ( L ) and ( K ) are the quantities of labor and capital, respectively. The prices of the two goods are ₦100 and ₦200, respectively. The firm's objective is to maximize its profit. Calculate the optimal quantities of labor and capital to use.