Consider a pricetaking rm that employs labour and capital to produce widgets. The rm's widget production technology can be represented by a production function of the form f (L, K) = min (aL, 5K), where L denotes the number of workers that are employed and K denotes the number of machines that are employed. Let Q demote the number of widgets that is both produced and sold by the rm. The rm faces a nite output price of $13 > 0 per widget, a nite wage rate for labour of $10 > 0 per worker, and a rental rate for capital of $7\" > 0 per machine. The rm's objective is to maximise its (economic) prot. 1. What is the rm's prot maximisation problem? 2. What is the rm's optimal supply of widgets as a function of the price vector (p, 1U,7')? 3. What is the rm's optimal unconditional demand for labour as a function of the price vector (p, 10,7\")? 4. What is the rm's optimal unconditional demand for capital as a function of the price vector (p, 10,7\")? 5. What is the rm's prot function