The manager of a supermarket meat department finds she has 200 lb of round steak, 800 lb of chuck steak, and 150 lb of pork in stock on saturday morning. she will use these to make three products: hamburger meat, picnic patties, and meatloaf. the demand for each of these items always exceeds the supermarket supply. therefore, she will be able to sell off all of however much of her current meat ingredients as she wants to. hamburger meat must consist of at least 20 percent round steak and at least 50 percent chuck steak by weight. picnic patties must consist of at least 20 percent pork and at least 50 percent chuck steak by weight. meatloaf must consist of at least 10 percent round steak, 30 percent pork, and 40 percent chuck. in each product, the remainder is an inexpensive filler, and the supermarket has an unlimited supply of it. the manager wants to know how much of each product she should produce so that the total amount of leftover meat ingredients that need to be carried over can be minimized. solve this problem using linear programming.