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.

b) What is the minimized level of total cost when output equals 12,800?