Operations Research - Study Mode
[#176] The occurrence of degeneracy while solving a transportation problem means that.
Correct Answer
(B) The solution so obtained is not feasible
Explanation
Solution: Degeneracy in a transportation problem occurs when there are fewer independent allocations than required, i.e., fewer than (m + n - 1) , where m is the number of rows and n is the number of columns. Option A: "Total supply equals total demand" is a necessary condition for feasibility but does not define degeneracy. Option B: "The solution is not feasible" is incorrect because degeneracy does not automatically lead to infeasibility. A valid solution can still exist despite degeneracy. Option C: "The few allocations become negative" is also incorrect because negative allocations are not allowed in a transportation problem. This would indicate an infeasible solution, which is unrelated to degeneracy. Therefore, the correct answer is Option D: None of the above, as none of the options accurately describe degeneracy. Degeneracy specifically refers to having too few independent allocations, which complicates the solution process but does not inherently make it infeasible.
[#177] An alternative optimal solution to a minimization transportation problem exists whenever opportunity cost corresponding to unused route of transportation is:
Correct Answer
(B) Positive with at least one equal to zero
Explanation
Solution: An alternative optimal solution to a minimization transportation problem exists whenever opportunity cost corresponding to unused route of transportation is Positive with at least one equal to zero.
[#178] As for maximization in assignment problem, the objective is to maximize the ___________.
Correct Answer
(A) Profit
Explanation
Solution: As for maximization in assignment problem, the objective is to maximize the Profit. An assignment problem is a particular case of transportation problem where the objective is to assign a number of resources to an equal number of activities so as to minimize total cost or maximize total profit of allocation.
[#179] Operations Research simply helps in improving the ______________ of the solution but does not in a perfect solution.
Correct Answer
(A) Quality
Explanation
Solution: Operations Research simply helps in improving the quality of the solution but does not in a perfect solution. It implies that by applying its scientific approach, it can only improve the quality of solution but it may not be able to give perfect solution.
[#180] Operations Research involves ______________ attack of complex problems to arrive at the optimum solution.
Correct Answer
(C) Both A and B
Explanation
Solution: Operations Research involves scientific and systematic attack of complex problems to arrive at the optimum solution. An optimal solution is a feasible solution where the objective function reaches its maximum (or minimum) value – for example, the most profit or the least cost. A globally optimal solution is one where there are no other feasible solutions with better objective function values.