Please answer to (c) because the question is related to (a) and (b) A company sells widgets in a perfectly competitive market. The market price for a widget is $100, while the cost of labour is $5 and that of capital is $8. The production function follows the Cobb-Douglas function below. Q = 0.220.5 (a) Using the Lagrangian multiplier method, find the profit maximizing quantity Q* and its associated profit. (b) The widget company was nationalized by the government and was asked to produce a total of Q** widgets such that (**>Q. The new CEO claims that by doing so, the profitability of the company will rise. Based on your previous finding, do you think this assertion is true? Explain. (c) Assuming that you became the CEO of the company and were told to produce *** number of widgets and would like to maximize the company's profit. How would you design the objective function, constraint and Lagrangian to ensure that the firm maximizes profit