The problem below involves three variables. Solve it with the simplex method, Excel, or some other technology.

Patio Iron makes wrought iron outdoor dining tables, chairs, and stools. Each table uses $8$ feet of a standard width wrought iron, $2$ hours of labor for cutting and assembly, and $2$ hours of labor for detail and finishing work. Each chair uses $6$ feet of the wrought iron, $2$ hours of cutting and assembly labor, and $1\mathrm{.}5$ hours of detail and finishing labor. Each stool uses $1$ foot of the wrought iron, $1\mathrm{.}5$ hours for cutting and assembly, and $0\mathrm{.}5$ hour for detail and finishing work, and the daily demand for stools is at most $22.$ Each day Patio Iron has available at most $138$ feet of wrought iron, $65$ hours for cutting and assembly, and $50$ hours for detail and finishing. If the profits are $$60$ for each dining table, $$48$ for each chair, and $$36$ for each stool, how many of each item should be made each day to maximize profit?

tables

chairs

stools

Find the maximum profit.