1. Problem: A manufacturer makes two models of an item, standard and deluxe. It costs $40 to manufacture the standard model, and $60 for the deluxe. A market research firm estimates that if the standard model is priced at x dollars, and the deluxe at y dollars, then the manufacturer will sell 500(y-x) of the standard items and 45000 + 500(x-2y) of the deluxe items each year. How should the items be priced to maximize profit? 2. Relevant equations: none 3. The attempt at a solution: I have f1x = -500, f1y = 500, and f2x = 500 and f2y = -1000 But none of these equations have critical points, so I know I'm supposed to check the boundaries next, but I don't know how to find them, or the absolute max. Also, never done this with two separate equations before, and I think that just means that I should do them seperately and use the points they have in common, but I'm not sure. Thanks for the help!