Attempt all questions. Correct answers are highlighted in yellow.
1.When there exists a non-basic variable in Big M method whose relative profit (i.e. cj) is zero in the optimal table, then the nature of the solution is?
a)
Unbounded
b)
Unique optimal
c)
Infeasible
d)
Alternate optimal
✓ Correct Answer
💡 Complete Solution & Explanation:
A zero relative profit for a non-basic variable indicates that there is more than one optimal solution (an alternate optimum) that can be reached by introducing that variable into the basis.
2.A supply at three sources is 80, 30 and 40 units respectively while the demand at the four destination is 30, 20, 25 and 55 units. In solving this transportation problem:
a)
dummy source of capacity 20 units is needed with unit transportation cost one.
b)
dummy destination of capacity 20 units is needed with unit transportation cost zero.
c)
dummy source of capacity 20 units is needed with unit transportation cost zero.
✓ Correct Answer
d)
dummy destination of capacity 20 units is needed with unit transportation cost one.
💡 Complete Solution & Explanation:
Total supply (80+30+40=150) is greater than total demand (30+20+25+55=130), so a dummy destination of capacity 20 units with zero cost would be added to balance the problem.
3.Degeneracy is not related with:
a)
Simplex method
b)
Assignment model
c)
Transportation model
d)
Sequencing
✓ Correct Answer
💡 Complete Solution & Explanation:
Degeneracy is a common issue in Linear Programming (Simplex method), Transportation problems, and Assignment problems (a special case of transportation). It is not typically a concern in sequencing models.
4.Dual of the dual problem is the:
a)
Primal
✓ Correct Answer
b)
Either primal of dual
c)
dual
d)
None of these
💡 Complete Solution & Explanation:
A fundamental property of linear programming duality is that the dual of the dual problem returns you to the original primal problem.
5.Arrival rate and departure rate should be.... to decrease Queue.
a)
Greater
✓ Correct Answer
b)
Departure should be lesser
c)
Arrival should be lesser
d)
System should be random
💡 Complete Solution & Explanation:
To decrease queue length and waiting time, the service or departure rate should be greater than the arrival rate (λ<μ).
Common queue disciplines include FIFO (First-In, First-Out), LIFO (Last-In, First-Out), and SIRO (Service in Random Order). \ ext{TESTING TO GET FASTER} is not a recognized standard queue discipline.
7.Transportation problem is basically a:
a)
Maximization problem
b)
Optimization
c)
Minimization problem
✓ Correct Answer
d)
Overestimation
💡 Complete Solution & Explanation:
The standard transportation problem is a specific type of Linear Programming problem where the objective is to minimize the total cost of transporting goods from sources to destinations.
8.Which of these is not used to get initial solution?
a)
NWCM
b)
VAN
c)
LCM
d)
MODI
✓ Correct Answer
💡 Complete Solution & Explanation:
The North-West Corner Method (NWCM), Vogel's Approximation Method (VAN), and Least Cost Method (LCM) are all used to find an initial basic feasible solution. The MODI (Modified Distribution) method is used for testing optimality and finding the optimal solution.
9.If an opportunity cost is used for an unusual cell to test optimality, for maximization it should be:
a)
Most nonnegative number
b)
any value
c)
Most positive number
✓ Correct Answer
d)
equal to 0
💡 Complete Solution & Explanation:
In the context of the Stepping Stone or MODI method, the cell with the most positive opportunity cost is chosen to enter the solution because it promises the largest reduction in total cost per unit shipped.
10.MODI method is used to solve:
a)
LPP problem
b)
Inventory problem
c)
Assignment problem
d)
Transportation problem
✓ Correct Answer
💡 Complete Solution & Explanation:
The MODI (Modified Distribution) method is a specialized technique used to find the optimal solution for a transportation problem after an initial basic feasible solution has been obtained.