A franchisee of Fuddruckers, a hamburger restaurant chain, has contracted to supply food for a daylong music festival. Fuddruckers distinguishes itself from other hamburger restaurant chains with on premise butcher shop and bakery. Suppose it is now the Wednesday before the Saturday festival. They have sold approximately 5,000 tickets so far, and this number should increase because weather forecast for Saturday is sunny. Based on previous experience, the manager believes that the eventual number of patrons and the associated probabilities are: Numbers 6,000 7,000 8,000 9,000 10,000 Probability .1 .2 .4 .2 .1 The manager expects that on average, each person will eat one meal during the seven-hour festival. She has decided to limit the menu to just two meals: burgers and hot dogs. She estimates, based on regular restaurant sales, that 60 percent of people will buy the burger and 40 percent will buy the hotdog. The cost of one burger will be $2.25 and it will sell for $5, whereas the hot dog will cost $1.34 and will sell for $4. She has to discard any unused food, and there is no penalty for being short. The meat, hot dogs, buns, and vegetables need to be ordered today (three days before the festival so that they will arrive on the day of the festival). Determine the optimal order quantity for burgers only.