3. A company sells widgets where the cost per unit of labor is $w, and the cost of capital is $r. The company's production technology is given the following Cobb-Douglas function Q=KaLb where Q is number of widgets produced, while K is the amount of capital used, and L is the total amount of labour employed. (a) Using the Lagrangian multiplier method, what is the cost minimizing quantity of capital K, and labour L given Q=Q ? (10 marks) (b) Assume that a=b=1,w=2,r=8, and Q=100. Using the Lagrangian multiplier, estimate the increase in cost (in terms of percentage) when production rises from 100 to 102 widgets