Question

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 1.5 hours of detail and finishing labor. Each stool uses 1 footof the wrought iron, 1.5 hours for cutting and assembly, and 0.5 hour for detail and finishing work, and the daily demand for stools is at most 16. Each day Patio Iron has available at most 156 feet of wrought iron, 70 hours for cutting and assembly, and 50 hours for detail and finishing. The profits are $60 for each dining table, $48 for each chair, and $36 for each stool.

Suppose Patio Iron wants to maximize its profits each day by making dining tables, chairs, and stools.

Let x be the number of dining tables, y be the number of chairs, and z be the number of stools made each day.

Let f be the maximum profit (in dollars). Form the profit equation that needs to be maximized.

f = ____

Since Patio Iron has available at most 156 feet of wrought iron, form the constraint inequality for the total feet of wrought iron used for dining tables, chairs, and stools.

___ ≤ 156

Since Patio Iron has available at most 70 hours for cutting and assembly, form the constraint inequality for the total hours spent on cutting and assembling dining tables, chairs, and stools.

___ ≤ 70

Since Patio Iron has available at most 50 hours for detail and finishing work, form the constraint inequality for the total hours spent on detailing and finishing dining tables, chairs, and stools.

___ ≤ 50

Since the daily demand for stools is at most 16,  ---Pick one--- x ≤ 16 or y ≤ 16 or z ≤ 16 .

How many of each item should be made each day to maximize profit? Solve with the simplex method, Excel, or some other technology.

tables ___

chairs ___

stools ___

Find the maximum profit.

$ ___

Answer 1

Then no.of dining tables,x1=1

No.of chair,x2=22

No.of stools,x3=16 is the optimal solution.

And maximum profit; max.f=1692

Thank you so much sir