Part A: Linear Programming

Question 1

What is linear programming?

Answer 1

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

Question 2

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

Answer 2

An objective function and constraints, expressed as linear inequalities.

Question 3

How are limitations on variables in linear programming expressed?

Answer 3

As linear inequalities, such as 𝑥≥10

Question 4

What does the objective function in linear programming represent?

Answer 4

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

Question 5

Write the general form of an objective function.

Answer 5

𝑍=𝑐1𝑥1+𝑐2𝑥2+⋯+𝑐𝑛𝑥𝑥𝑛

Z=∑ n, i=1: ci xi

Question 6

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

Answer 6

They are the decision variables of the objective value Z.

Question 7

In the objective function, what do 𝑐1 , 𝑐2 represent

Answer 7

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

Question 8

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

Answer 8

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

Question 9

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

Answer 9

To find the maximum value for Z

Question 10

Describe the form of constraints in linear programming

Answer 10

Constraints are expressed as inequalities, such as 𝑥1≤100.000