Consider a firm producing two types of luxury pet foods: dog food and cat food. Let x be the daily quantity of dog food produced and let y be the daily quantity of cat food produced. Suppose that the firm is facing the following profit (z) function: (, ) = 10 5 2 20 7 2 + 240 5300 How much dog food and how much cat food should the firm produce daily to maximize profit? Find the profit maximizing output of each good. Show your work. Make sure you prove that profit is, indeed, maximized