# linear programming Flashcards

Browse 453 sets of linear programming flashcards

Standard Form for a linear equation

system of linear inequalities

linear programming

linear inequality

A particular form for a linear equation

two more linear inequalities using the same defined variables

a technique used for maximizing or minimizing an objective fun…

The solution to a linear inequality is a "half plane" - the co…

Standard Form for a linear equation

A particular form for a linear equation

system of linear inequalities

two more linear inequalities using the same defined variables

The vertices of a feasible region are (…

The constraints of a problem are graphe…

Joey is buying plants for his garden. H…

The constraints of a problem are listed…

C. 3,080

A. (0, 0), (0, 15), (20, 25), (40, 0)

(24, 12), (36, 0)

D. (0, 1), (0, 7), (4, 3)

The vertices of a feasible region are (…

C. 3,080

The constraints of a problem are graphe…

A. (0, 0), (0, 15), (20, 25), (40, 0)

X- Intercept... Y- Intercept... Horizonal Lin…

Slope- Intercept form of the equation o…

Slope of the line

Intersection

Let Y=0... Let X=0... Y=K... X=C

a linear equation written as y=mx+b, where m is the slope and…

Rise over run

A point where lines intersect.

X- Intercept... Y- Intercept... Horizonal Lin…

Let Y=0... Let X=0... Y=K... X=C

Slope- Intercept form of the equation o…

a linear equation written as y=mx+b, where m is the slope and…

Optimization

Linear programming

Objective function

Constraints

Finding a minimum or maximum value

Optimize subject to a set of constraints

Linear function being optimized

System of linear inequalities representing the limitation

Optimization

Finding a minimum or maximum value

Linear programming

Optimize subject to a set of constraints

C. 3,080

(24, 12), (36, 0)

D. (0, 1), (0, 7), (4, 3)

A. 1/3x + 1/2y < or equal to 12... 2x + y…

The vertices of a feasible region are (14, 2), (0, 9), (6, 8),…

Joey is buying plants for his garden. He wants to have at leas…

The constraints of a problem are listed below. What are the ve…

Alan wants to bake blueberry muffins and bran muffins for the…

C. 3,080

The vertices of a feasible region are (14, 2), (0, 9), (6, 8),…

(24, 12), (36, 0)

Joey is buying plants for his garden. He wants to have at leas…

The vertices of a feasible region are (…

The constraints of a problem are graphe…

Joey is buying plants for his garden. H…

The constraints of a problem are listed…

3,080

(0, 0), (0, 15), (20, 25), (40, 0)

(24, 12), (36, 0)

(0, 1), (0, 7), (4, 3)

The vertices of a feasible region are (…

3,080

The constraints of a problem are graphe…

(0, 0), (0, 15), (20, 25), (40, 0)

Standard Form for a linear equation

system of linear inequalities

linear programming

linear inequality

A particular form for a linear equation

two more linear inequalities using the same defined variables

a technique used for maximizing or minimizing an objective fun…

The solution to a linear inequality is a "half plane" - the co…

Standard Form for a linear equation

A particular form for a linear equation

system of linear inequalities

two more linear inequalities using the same defined variables

Standard Form for a linear equation

system of linear inequalities

linear programming

linear inequality

A particular form for a linear equation

two more linear inequalities using the same defined variables

a technique used for maximizing or minimizing an objective fun…

The solution to a linear inequality is a "half plane" - the co…

Standard Form for a linear equation

A particular form for a linear equation

system of linear inequalities

two more linear inequalities using the same defined variables

Standard Form for a Linear Equation

System of Linear Inequalities

Linear Programming

Feasible Region

A particular form for a linear equation

two more linear inequalities using the same defined variables

a technique used for maximizing or minimizing an objective fun…

The shaded area that results from the intersecting graphs of t…

Standard Form for a Linear Equation

A particular form for a linear equation

System of Linear Inequalities

two more linear inequalities using the same defined variables

Feasible region

constraints

bounded, minimum and maxium, vertex

linear programming

the intersection of the graph of a system on inequalities

the inequalities which define the feasible region

when a system of linear inequalites produces a ______________…

the process of finding the minimum or maximum values of the fu…

Feasible region

the intersection of the graph of a system on inequalities

constraints

the inequalities which define the feasible region

Optimization

Linear programming

Objective function

Constraints

Finding a minimum or maximum value

Optimize subject to set of constraints

Linear function being optimized

System of linear inequalities

Optimization

Finding a minimum or maximum value

Linear programming

Optimize subject to set of constraints

Standard Form for a linear equation

system of linear inequalities

linear programming

linear inequality

A particular form for a linear equation

two more linear inequalities using the same defined variables

a technique used for maximizing or minimizing an objective fun…

The solution to a linear inequality is a "half plane" - the co…

Standard Form for a linear equation

A particular form for a linear equation

system of linear inequalities

two more linear inequalities using the same defined variables

Alternative Optimal Solutions

Constraint

Extreme Point

Feasible Region

The case in which more than one solution provides the optimal…

An equation or inequality that rules out certain combinations…

Graphically speaking, extreme points are the feasible solution…

The set of all feasible solutions

Alternative Optimal Solutions

The case in which more than one solution provides the optimal…

Constraint

An equation or inequality that rules out certain combinations…

Objective Function

Variables

Vertices

inequality

The function being maximized or minimized in Linear Programming

letters used to represent unknown quantities

The vertices of the shaded shape you created

A mathematical sentence that contains less than or greater than

Objective Function

The function being maximized or minimized in Linear Programming

Variables

letters used to represent unknown quantities

decision variables

objective function

constraints

shadow prices

controllable input variable that represents the key decisions…

the expression that defines the quantity to be maximized or mi…

a limitation or requirement that must be satisfied by the solu…

maximum price that management is willing to pay for an extra u…

decision variables

controllable input variable that represents the key decisions…

objective function

the expression that defines the quantity to be maximized or mi…

Why Use Linear Programming?

Examples of LP Applications

Requirements of an LP Problem

Three types of constraints

a mathematical technique to help plan and make decisions relat…

1) scheduling school buses to MINIMIZE total distance traveled…

1) LP problems seek to maximize or minimize some quantity expr…

1) Upper limits (<=)- often resource limits, max... 2) Lower lim…

Why Use Linear Programming?

a mathematical technique to help plan and make decisions relat…

Examples of LP Applications

1) scheduling school buses to MINIMIZE total distance traveled…

Why use linear programming (LP)?... a.Math…

Examples of Linear Programming

Requirements of an LP problem... a.Seek to…

Three types of constraints... •________ li…

...

Airlines and flight crews, Product mix, Bank tellers, Distribu…

objective function; constraints; linear equations; inequalities

Upper; Lower; Equalities

Why use linear programming (LP)?... a.Math…

...

Examples of Linear Programming

Airlines and flight crews, Product mix, Bank tellers, Distribu…

Decision variables

Non-negativity

Linear programming

In maximization, this is the sign.

It represents choices available in terms of amount of either i…

It cannot use or produce negative physical quantities.

A mathematical procedure for determining optimal allocation of…

Less than or equal to

Decision variables

It represents choices available in terms of amount of either i…

Non-negativity

It cannot use or produce negative physical quantities.

Slack variables

Z

Forming an initial tableau

Finding pivot column

What you need to add to inequalities to make them equations e.…

Letter used for maximum/minimum function

Make the objective function equal to 0 (put all terms on one s…

Choosing the most negative coefficient in the objective functi…

Slack variables

What you need to add to inequalities to make them equations e.…

Z

Letter used for maximum/minimum function

A botanist is using two types of plants…

Joey is buying plants for his garden. H…

The vertices of a feasible region are (…

Alan wants to bake blueberry muffins an…

a. Buying five of one type of plant and 39 of the other type o…

d. (24, 12), (36, 0)

c. 3,080

a. ... 1/3x + 1/2y ≤ 4... 2x + y ≤ 12... x ≥ 0... y ≥ 0

A botanist is using two types of plants…

a. Buying five of one type of plant and 39 of the other type o…

Joey is buying plants for his garden. H…

d. (24, 12), (36, 0)

What is an objective?

What are constraints?

What is solver?

Why would you choose an Int constraint?

It is an equation we wish to minimize/maximize (optimize).

It's the limited resources/conditions that must be met.

It is a linear program that uses the Simplex Algorithm

To get you whole number answers in the optimal solution.

What is an objective?

It is an equation we wish to minimize/maximize (optimize).

What are constraints?

It's the limited resources/conditions that must be met.

Constraints

Feasible Region

Linear Programming

Objective Function

limits or restrictions

intersection of the inequalities (shaded region) that contains…

A method for finding a minimum or maximum value of some quanti…

The mathematical equation that defines the quantity to be maxi…

Constraints

limits or restrictions

Feasible Region

intersection of the inequalities (shaded region) that contains…

The vertices of a feasible region are (…

The constraints of a problem are graphe…

Joey is buying plants for his garden. H…

The constraints of a problem are listed…

3,080

(0, 0), (0, 15), (20, 25), (40, 0)

(24, 12), (36, 0)

(0, 1), (0, 7), (4, 3)

The vertices of a feasible region are (…

3,080

The constraints of a problem are graphe…

(0, 0), (0, 15), (20, 25), (40, 0)

How do you decide on your x and y (and…

How do you solve an optimisation proble…

If you are looking at a maximise proble…

If you are looking at a minimise proble…

The things that the you are deciding on how many you need to m…

Formulate inequalities and set them as line equations by makin…

The vertex further away from the origin

The vertex further nearest to the origin

How do you decide on your x and y (and…

The things that the you are deciding on how many you need to m…

How do you solve an optimisation proble…

Formulate inequalities and set them as line equations by makin…

Goal of LP

Programming

Linear

Linear Programming

Minimize costs or maximize profits

The planning, scheduling, or performing of a program

Mathematically, a linear function is a polynomial of degree ze…

A method to achieve the best outcome

Goal of LP

Minimize costs or maximize profits

Programming

The planning, scheduling, or performing of a program