Linear Programming Flashcards

1
Q

What is linear programming?

A

Linear programming is a mathematical method for finding optimal solutions to problems such as maximizing profit or minimizing costs.

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2
Q

What components are used in linear programming to define the problem?

A

An objective function and constraints, expressed as linear inequalities.

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3
Q

How are limitations on variables in linear programming expressed?

A

As linear inequalities, such as 𝑥≥10

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4
Q

What does the objective function in linear programming represent?

A

It represents the value (profit, time, cost) that we want to optimize.

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5
Q

Write the general form of an objective function.

A

𝑍=𝑐1𝑥1+𝑐2𝑥2+⋯+𝑐𝑛𝑥𝑥𝑛

Z=∑ n, i=1: ci xi

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6
Q

In the objective function 𝑍 what do 𝑥1 , 𝑥2 represent?

A

They are the decision variables of the objective value Z.

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7
Q

In the objective function, what do 𝑐1 , 𝑐2 represent

A

They are coefficients that show the impact of each decision variable.

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8
Q

Provide an example of an objective function for maximizing profit from selling two products.

A

Z=5x1 + 3x2 , where the profits are $5 and $3 per unit for products 𝑥1 and x2 ​ respectively.

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9
Q

What is the goal when solving a maximization problem in linear programming?

A

To find the maximum value for Z

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10
Q

Describe the form of constraints in linear programming

A

Constraints are expressed as inequalities, such as 𝑥1≤100.000

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