Post Utme Redeemers University 2024 Commerce Question 20

A firm is considering two different production technologies: one that uses labor and capital as inputs, and another that uses only labor as an input. The production function for the first technology is given by the equation ( Q = 100L^0.5K^0.25 ), while the production function for the second technology is given by the equation ( Q = 50L^0.5 ). If the firm wants to produce 100 units of the commodity, and the wage rate is ₦100 per hour, while the rental rate for capital is ₦50 per hour, what is the minimum cost of production for each technology?