BSIE Operations Research & Linear Programming

Question 1

In linear programming, what is the region that satisfies all constraints called?

Accepted Answer

Feasible region

Answer

The feasible region is the set of all points that satisfy every constraint in a linear programming problem.

Question 2

Which method is most commonly used to solve large-scale linear programming problems?

Accepted Answer

Simplex method

Answer

The simplex method iterates along the edges of the feasible polytope to find the optimal vertex efficiently for large-scale LP problems.

Question 3

In the transportation problem, what condition must be met for a balanced problem?

Accepted Answer

Total supply equals total demand

Answer

A balanced transportation problem requires that the sum of all supplies equals the sum of all demands.

Question 4

What does the dual price (shadow price) represent in linear programming?

Accepted Answer

The rate of change of the objective function per unit increase in a constraint's RHS

Answer

The shadow price tells the decision-maker how much the optimal objective value improves for each one-unit relaxation of a binding constraint.

Question 5

In queuing theory, what does the notation M/M/1 represent?

Accepted Answer

Markovian arrivals, Markovian service, 1 server

Answer

M/M/1 denotes a queue with Poisson (Markovian) arrivals, exponential (Markovian) service times, and a single server.

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