Feasible Regions
Graph it!
Constraints
Max Prof
100
What is a feasible region?
The darkest shaded area where all of the constraints overlap. All points in the shaded area are possible solutions to problem.
100
Where do we find the vertices?
They are the corner points of the feasible region.
100
What are constraints?
Constraints are the inequalities in a linear programming model. They often come from the restrictions placed on available resources.
100
What is an objective function?
An equation that helps determine what the maximum or minimum is. It is usually about profit.
200
Select the feasible region for the constraints listed below:
x-y>=-1
2x+3y<=12
x>=0
C
200
List the vertices of the graph below:
(0,2)
(4,-2)
(-4,-2)
200
Potomac Clothing Co. makes two types of clothes and has an alteration and tailoring department. Dresses take 2 hours to alter and four hours to tailor. Suits take 4 hours to alter and 6 hours to tailor. The alterations department only has 32 hours of labor per day and the tailoring department only has 56 hours of labor per day. Potomac Clothing Co. makes a profit of $50 per dress and $150 per suit. How many dress and suits should Potomac Clothing Co. make in order to maximize profit?
Write a constraint about the amount of hours the alterations department works.
2x+4y<=32
200
Potomac Clothing Co. makes two types of clothes and has an alteration and tailoring department. Dresses take 2 hours to alter and four hours to tailor. Suits take 4 hours to alter and 6 hours to tailor. The alterations department only has 32 hours of labor per day and the tailoring department only has 56 hours of labor per day. Potomac Clothing Co. makes a profit of $50 per dress and $150 per suit. How many dress and suits should Potomac Clothing Co. make in order to maximize profit?
What is the objective function?
P = 50x+150y
300
Select the feasible region that represents the following constraints:
y+2x<=5
y>=0
x >= 0
-x+y<=4
C
300
List the vertices for the feasible region below:
(2,0)
(6,0)
(6,3)
(2,5)
300
Potomac Clothing Co. makes two types of clothes and has an alteration and tailoring department. Dresses take 2 hours to alter and four hours to tailor. Suits take 4 hours to alter and 6 hours to tailor. The alterations department only has 32 hours of labor per day and the tailoring department only has 56 hours of labor per day. Potomac Clothing Co. makes a profit of $50 per dress and $150 per suit. How many dress and suits should Potomac Clothing Co. make in order to maximize profit?
Write a constraint about the tailoring department.
4x+6y<=56
300
Potomac Clothing Co. makes two types of clothes and has an alteration and tailoring department. Dresses take 2 hours to alter and four hours to tailor. Suits take 4 hours to alter and 6 hours to tailor. The alterations department only has 32 hours of labor per day and the tailoring department only has 56 hours of labor per day. Potomac Clothing Co. makes a profit of $50 per dress and $150 per suit.
How many dress and suits should Potomac Clothing Co. make in order to maximize profit?
Potomac Clothing Co. should make 0 dresses and 8 suits in order to maximize profit.
400
Identify all of the points that could be considered solutions to the constraints listed below:
-8x-12y>=-192
y>=4 x>=3
(0,0) (18,4) (10,6) (5,11) (20,5)
(18,4) (10,6) (5,11)
400
Graph the constraints and list the points that make up the feasible region:
y>=3
x>=4
x+y<=24
y-1/2x<=12
(4,3)
(4,14)
(8,16)
(21,3)
400
Potomac Laundromat offers laundry washing services. To make a profit, the laundromat charges $5.50 per small load and $7 per large load of laundry. Small loads of laundry take 2 hours to wash, and large loads of laundry take 4 hours to wash. The Laundromat only has 36 hours for washing laundry and has a maximum capacity of 15 total loads of laundry. The laundromat must also wash a minimum of 2 small loads of laundry and a minimum of 1 large load of laundry. How many of each type of load should the laundromat wash to maximize profit?
Write 4 constraints.
2x+4y <=36
x+y<=15
y>=1
x>=2
400
Potomac Laundromat offers laundry washing services. To make a profit, the laundromat charges $5.50 per small load and $7 per large load of laundry. Small loads of laundry take 2 hours to wash, and large loads of laundry take 4 hours to wash. The Laundromat only has 36 hours for washing laundry and has a maximum capacity of 15 total loads of laundry. The laundromat must also wash a minimum of 2 small loads of laundry and a minimum of 1 large load of laundry.
How many of each type of load should the laundromat wash to maximize profit?
Potomac Laundromat must wash 12 small loads and 3 large loads of laundry in order to maximize profit.