Exercise $7$ Use the method of linear programming to solve the problem.

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 $(2400$ minutes 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 the maximum profit?

Step $1$: List the independent variables.

$x=$

$y=$