Post Utme Greenfield University 2022 Economics Question 39

A farmer produces wheat and corn on a 100-hectare farm. The production function for wheat is given by Qw = 2L^0.5K^0.5, where Qw is the quantity of wheat produced, L is the labor input, and K is the land input. The production function for corn is given by Qc = 3L^0.5K^0.5, where Qc is the quantity of corn produced. If the farmer wants to produce 50 units of wheat and 75 units of corn, and the wage rate is ₦100 per hour, and the rental rate of land is ₦200 per hectare, what is the optimal combination of labor and land that the farmer should use?