Consider a price-taking firm that employs labour and capital to produce widgets. The firm's widget production technology can be represented by a production function of the form f (L, K') = min (aL, BK), where L denotes the number of workers that are employed and K denotes the number of machines that are employed. Let () demote the number of widgets that is both produced and sold by the firm. The firm faces a finite output price of $p > 0 per widget, a finite wage rate for labour of $w > 0 per worker, and a rental rate for capital of $7 > 0 per machine. The firm's objective is to maximise its (economic) profit. 1. What is the firm's profit maximisation problem? 2. What is the firm's optimal supply of widgets as a function of the price vector (p,w,r)? 3. What is the firm's optimal unconditional demand for labour as a function of the price vector (p,w,r)? 4. What is the firm's optimal unconditional demand for capital as a function of the price vector (p,w,r)? 5. What is the firm's profit function