Mathematics · Economics

Optimization and Mathematical Programming

1,582 Questions

Mathematical programming involves selecting the best element from a set of alternatives based on specific criteria. These concepts are tested in various competitive exams, especially those focusing on decision making and resource allocation. The collection includes problems on linear programming, structural optimization, and computational complexity.

Linear programmingDynamic programmingConvex optimizationInteger programmingStructural optimization methodsMathematical modeling

Optimization and Mathematical Programming Questions

Multiple choice

To decide the departing variable in a simplex table giving a non-optimum solution, the least non-negative replacement ratio is selected.

  1. TRUE

  2. FALSE
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The minimum ratio test (least non-negative ratio) determines which variable reaches zero first as the entering variable increases. This selection ensures that feasibility is maintained - the chosen departing variable becomes non-basic while all other basic variables remain non-negative.

Multiple choice

Heuristic function is also called

  1. probability function

  2. optimal function

  3. objective function

  4. linear function
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In optimization and search, the heuristic function is often referred to as the objective function because it defines the goal or the 'cost' that the algorithm aims to minimize or maximize.

Multiple choice

__________ is a useful variation on Simple Hill-Climbing that considers all the moves from the current state and selects the best one as the next state.

  1. Complex Hill-Climbing

  2. Steepest-Ascent Hill-Climbing

  3. Simulated Annealing

  4. None of the above
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Steepest-Ascent Hill-Climbing evaluates all possible successors of the current state and chooses the one that provides the greatest improvement, rather than just taking the first better move found.

Multiple choice

The cryptarithmetic puzzle is an example for

  1. problem reduction

  2. constraint satisfaction

  3. best-first-search

  4. all of the above
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Cryptarithmetic puzzles require assigning digits to letters such that the arithmetic holds true, which is a classic example of a constraint satisfaction problem where each letter is a variable with constraints on its possible values.

Multiple choice

__________ strategy reasons both in forward and backward directions.

  1. Constraint satisfaction

  2. Hill-climbing search

  3. Generate & test

  4. Means-ends analysis
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Means-ends analysis is a problem-solving strategy that compares the current state to the goal state and identifies the differences, working both forward from the current state and backward from the goal to bridge the gap.

Multiple choice

The expected time (te) of a PERT activity in terms of optimistic time (t0), pessimistic time (tp) and most Likely time (tl) is given by
  1. te = $\frac{t_o + 4t_1 + t_p}{6}$
  2. te = $\frac{t_o + 4t_p + t_{p1}}{6}$
  3. te = $\frac{t_o + 4t_1 + t_p}{3}$
  4. te = $\frac{t_o + 4t_1 + t_1}{3}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Under the conditions of uncertainty, the estimated time for each activity for PERT network is represented by a probability distribution. This probability distribution