Vermont Farm Table produces custom tables within its manufacturing facilities. Because of its history and experience, it is capable of renting its equipment and hiring workers at competitive rates. Labour is hired at $ 12 per hour and equipment is rented at $ 48 per hour. The manufacturing company has allocated $ 200,000 as a budget in order to complete its initial orders needed for the first quarter of the year. The production function used is the following :

Q= 0.25K^0.2 L^0.8

- Find the optimal input ratio in the long run -Determine the input mix needed to obtain the greatest output for a cost of $200,000. Determine the level of output. -Calculate the input mix in the short run, while keeping capital fixed, if production of tables were increased by 200 units. -Calculate the new cost of production in the short-run. -Draw the isoquants and isocost line, showing both the long-term and short-term mix. Ensure that the graph is properly labelled.