A firm uses labour whose quantity is denoted by ? and capital services whose quantity is denoted by ?. The production function is given by ? = 100??, and the price of labour ? is $2 per unit and the price of capital ? is $1 per unit. a) Using the method of Lagrange, find the firm's cost-minimizing input combination (?,?) when it seeks to produce 12,800 units per year. (15 marks) b) What is the minimized level of total cost ?? when output equals 12,800