Chapter 12.1, Problem 19E

How much of her available time would be unused if the craftswoman of Exercise $7$ maximizes her profit? How much of her available money would be unused?

7. A craftswoman produces two products: floor lamps and table lamps. Production of one floor lamp requires 75 minutes of her labor and materials that cost $\$25$. Production of one table lamp requires $50$ minutes of labor, and the materials cost $\$20$. The craftswoman wishes to work no more than $40$ hours each week, and her financial resources allow her to pay no more than $\$900$ for materials each week. If she can sell as many lamps as she can make and if her profit is $\$39$ per floor lamp and $\$33$ per table lamp, how many floor lamps and how many table lamps should she make each week to maximize her weekly profit? What is that maximum profit?