Лінійне програмування

What is linear programming?

• A technique for data analysis

• A mathematical optimization technique

• A method for solving algebraic equations

• A computer programming language

What are the basic components of a linear programming problem?

• objective function, decision variables, constraints, non-linear region

• objective function, decision variables, constraints, unbounded region

• objective function, decision variables, constraints, infeasible region

• objective function, decision variables, constraints, feasible region

What is the difference between an objective function and constraints in linear programming?

• The objective function represents the goal or objective of the problem, while constraints are the conditions or limitations that must be satisfied.

• The objective function is a condition, while constraints are the limitations.

• The objective function and constraints are the same thing.

• The objective function is a limitation, while constraints represent the goal.

What is the feasible region in linear programming?

• The feasible region is the set of all possible solutions that satisfy some of the constraints of the problem.

• The feasible region is the set of all impossible solutions that do not satisfy any of the constraints of the problem.

• The feasible region is the set of all possible solutions that satisfy none of the constraints of the problem.

• The feasible region is the set of all possible solutions that satisfy all the constraints of the problem.

What is the graphical method used for in linear programming?

• To calculate the objective function.

• To determine the constraints of the problem.

• To visually represent the feasible region and find the optimal solution.

• To identify the decision variables.

What are the steps involved in solving a linear programming problem using the simplex method?

• The steps involved in solving a linear programming problem using the simplex method are: formulate the problem, convert inequalities, set up initial tableau, choose pivot column and row, update tableau, repeat pivot steps, interpret final tableau, perform sensitivity analysis, and verify the solution.

• Set up the initial tableau, choose pivot column and row randomly, update tableau, repeat pivot steps until the solution is found, and interpret the final tableau.

• Convert the problem into a non-linear equation, solve the equation using calculus, interpret the solution, and verify the solution.

• Formulate the problem, convert equations, set up initial tableau, choose pivot column and row, update tableau, repeat pivot steps, interpret final tableau, perform sensitivity analysis, and verify the solution.

What is duality in linear programming?

• Relationship between the primal and dual problems

• The relationship between the primal and dual variables

• The process of converting a primal problem into a dual problem

• A mathematical technique used in linear programming

What is sensitivity analysis in linear programming?

• Process of analyzing the sensitivity of the objective function in linear programming.

• Method used to find the maximum value in linear programming.

• Technique used to determine the feasibility of a linear programming problem.

• Technique used to determine how changes in input parameters affect the optimal solution.

What is the difference between primal and dual problems in linear programming?

• The primal problem maximizes the objective function, while the dual problem minimizes the objective function.

• The primal problem has constraints in terms of variables, while the dual problem has constraints in terms of resources.

• The primal problem is the original problem, while the dual problem is derived from the primal problem.

• The primal problem is solved using the simplex method, while the dual problem is solved using the interior point method.

How can you interpret the shadow price in linear programming?

• The shadow price represents the maximum allowable increase in the right-hand side of a constraint.

• The shadow price represents the cost of producing an additional unit of a resource.

• The shadow price represents the rate of change in the objective function value with respect to a unit increase in the right-hand side of a constraint.

• The shadow price represents the minimum allowable decrease in the objective function value.