Assume a garment factory has the production function = KL^2. The factory initially faces input prices w = $1 and r = $2 and is required to produce Q = 2000 units. Later the price of labour w goes up to $4.

Find:

a) the initial optimal input bundle

b) the new optimal input bundle following the increase in the wage rate. (Hint: You can round off your answers to the nearest whole number).