The problem below involves three variables. Solve it with thesimplex 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 widthwrought iron, 2 hours of labor for cutting and assembly, and 2hours of labor for detail and finishing work. Each chair uses 6feet of the wrought iron, 2 hours of cutting and assembly labor,and 1.5 hours of detail and finishing labor. Each stool uses 1footof the wrought iron, 1.5 hours for cutting and assembly, and0.5 hour for detail and finishing work, and the daily demand forstools is at most 16. Each day Patio Iron has available atmost 156 feet of wrought iron, 70 hours for cutting and assembly,and 50 hours for detail and finishing. The profits are $60 for eachdining table, $48 for each chair, and $36 for each stool.
Suppose Patio Iron wants to maximize its profits eachday by making dining tables, chairs, and stools.
Let x be the number of dining tables, y be thenumber of chairs, and z be the number of stools made eachday.
Let f be the maximum profit (in dollars). Form theprofit equation that needs to be maximized.
f = ____
Since Patio Iron has available at most 156 feet ofwrought iron, form the constraint inequality for the total feet ofwrought iron used for dining tables, chairs, and stools.
___ ? 156
Since Patio Iron has available at most 70 hours forcutting and assembly, form the constraint inequality for the totalhours spent on cutting and assembling dining tables, chairs, andstools.
___ ? 70
Since Patio Iron has available at most 50 hours fordetail and finishing work, form the constraint inequality for thetotal hours spent on detailing and finishing dining tables, chairs,and stools.
___ ? 50
Since the daily demand for stools is at most16, ---Pick one--- x ? 16 or y ? 16 or z ? 16 .
How many of each item should be made each day to maximizeprofit? Solve with the simplex method, Excel, or some othertechnology.
tables ___
chairs ___
stools ___
Find the maximum profit.
$ ___
