Tom owns a business. He knows that the production function(q) requires workers(L) and machines (K), and L and K are perfect complements. A worker can work on 2 product per hour. That is, the production function per hour is q = min(2L, 2K) . The wage of a worker per hour is w = 30, and the cost of using a machine for an hour is r = 5 . First, suppose we are in the short run, and Tom has 10 machine.

a) Draw Tom's production function, plotting the number of workers (L) on the x-axis and the number of output per hour (q) on the y-axis. For the rest of the question, suppose we are in the long run, so Tom can choose both the number of workers and machine.

b) Tom wants to provide 30 pet grooms per hour in her salon. How much K and L should be used to minimize costs? What is her cost per hour for those 30 pet grooms?

c) What is the business's total long-run cost function for output per hour as a function of its quantity q?