You own a hamburger stand, “Two Guys”. (You don’t have any partner, but “Two Guys” sounds better than “One Guy” or “Just a Guy”.). Your specialty is delicious cheeseburger that you sell for $6.50 a piece. The cost of ingredients for each cheeseburger, such as meat, buns, tomato etc., is $1.50. You hire workers at $12 an hour. The production function for cheeseburgers is Q=40\sqrt{L} , where L is the number of labor hours employed and Q the number of cheeseburgers produced. There is a fixed cost of $168. (a) There is no way to produce delicious cheeseburgers without also producing lots of grease, which needs to be hauled away. In fact every cheeseburger that you produce, you also produce 1 ounce of grease. You hire a service that hauls away grease at the cost of $3.20 per pound. Calculate the profit maximizing number of hamburgers, the amount of grease produced, the number of labor hours used and the consequent level of profit. (b) Suddenly, cooking grease has become popular as an ingredient to produce alternative fuel. So a company begins to buy grease from you every day at the rate of $1.60 per pound, thereby eliminating your cost of hauling away grease and also providing you another revenue source. Calculate the profit maximizing number of hamburgers, the amount of grease produced, the number of labor hours used and the consequent level of profit