The production function of a firm is given by q= KL.Input prices are as follow: rental rate on capital r = 3 and wage is w = 2.In long run, both inputs are variables.

a) Please find the combination of the inputs (K &L) that minimizes total cost of producing 200 units of output.What is the total cost of producing 200 units of output? Show your calculation step by step.

b) If the wage rate goes up to 3, find the new combination of the inputs and write down the total cost function. Show your calculation step by step.