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

Patio Ironmakes wrought iron outdoor dining tables, chairs, and stools. Each table uses8 feetof a standard width wrought iron,2 hoursof labor for cutting and assembly, and2 hoursof labor for detail and finishing work. Each chair uses6 feetof the wrought iron,2 hoursof cutting and assembly labor, and1.5 hoursof detail and finishing labor. Each stool uses1 footof the wrought iron,1.5 hoursfor cutting and assembly, and0.5 hourfor detail and finishing work, and the daily demand for stools is at most 16. Each dayPatio Ironhas available at most156feetof wrought iron,70hoursfor cutting and assembly, and50hoursfor detail and finishing. The profits are $60 for each dining table, $48 for each chair, and $36 for each stool.

SupposePatio Ironwants to maximize its profits each day by making dining tables, chairs, and stools.

Letxbe the number of dining tables,ybe the number of chairs, andzbe the number of stools made each day.

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

f=

SincePatio Ironhas available at most156feet of wrought iron, form the constraint inequality for the total feet of wrought iron used for dining tables, chairs, and stools.

156

SincePatio Ironhas available at most70hours for cutting and assembly, form the constraint inequality for the total hours spent on cutting and assembling dining tables, chairs, and stools.

70

SincePatio Ironhas available at most50hours 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,

---Select---

x 16

y 16

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.

tableschairsstools

Find the maximum profit.

$

At one of its factories, a manufacturer of college logo sweatshirts makes two styles: crewneck pullover and hooded. Each pullover sweatshirt takes5 minutesto cut out and20 minutesto assemble and finish. Each hooded sweatshirt takes5 minutesto cut out and30 minutesto assemble and finish. The plant has enough workers to provide at most3,750 minutesper day for cutting and at most19,500 minutesper day for assembly and finishing. The profit on each pullover sweatshirt is $6and the profit on each hooded sweatshirt is $8. How many of each sweatshirt should be produced each day to obtain maximum profit? Find the maximum daily profit.

pulloversweatshirtshoodedsweatshirtsprofit$