Chapter 13.8, Problem 44ES

A manufacturer makes two models of an item, standard and deluxe. It costs $\text{\$40}$ to manufacture the standard model and $\text{\$60}$ 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 $500\left(y-x\right)$ of the standard items and $45,000+500\left(x-2y\right)$ of the deluxe each year. How should the items be priced to maximize the profit?