Q21 Simplex method of solving linear programming problem uses

(a) all the points in the feasible region 
(b) only the corner points of the feasible region 
(c) intermediate points within the infeasible region 
(d) only the interior points in the feasible region.

Ans: (b) only the corner points of the feasible region


Q22. Cars arrive at a service station according to Poisson’s distribution with a mean rate of 5 perh ur. The service time per car is exponential with a mean of 10 minutes. At state, the average waiting time in the queue is

(a) 10 min 
(b) 20 min 
(c) 25 min 
(d) 50 min.                                                                              (GATE-ME-2011)

Ans:  (d) 50 min.


Q23. Capacities of production of an item over 3 consecutive months in regular time are 100, 100 and 80 and in overtime are 20, 20 and 40. The demands over those 3 months are 90, 130 and 110. The cost of production in regular time and overtime are respectively ` 20 per item and` 24 per item. Inventory carrying cost is ` 2 per item per month. The levels of starting and final inventory are nil. Backorder is not permitted. For minimum cost of plan, the level of planned production in overtime in the third month is

(a) 40 
(b) 30 
(c) 20 
(d) 0.                                                                                            (GATE-ME-2007)

Ans:  (b) 30


Q24. For the standard transportation linear programme with m sources and n destinations and total supply equaling total demand, an optimal solution (lowest cost) with the smallest number of non-zero xij values (amounts from source i to destination j) is desired. The best
upper bound for this number is

(a) mn 
(b) 2(m + n) 
(c) m + n 
(d) m + n – 1.                                                                              (GATE-ME-2008)

Ans:  (d) m + n – 1. 


Q25. Annual demand for window frames is 10000. Each costs ` 200 and ordering cost is ` 300 per order. Inventory holding cost is ` 40 per frame per year. The supplier is willing to offer 2% discount if the order quantity is 1000 or more, and 4% if order quantity is 2000 or more. If the total cost is to be minimized, the retailer should

(a) order 200 frames every time 
(b) accept 2% discount 
(c) accept 4% discount 
(d) order economic order quantity.                                            (GATE-ME-2010)

Ans:  (c) accept 4% discount


Q26. Customers arrive at a ticket counter at a rate of 50 per hr and tickets are issued in the order of their arrival. The average time taken for issuing a ticket is 1 min. Assuming that customer arrivals form a Poisson process and service times are exponentially distributed, the average waiting time in queue in min is

(a) 3 
(b) 4 
(c) 5 
(d) 6.                                                                                                     (GATE-ME-2013)

Ans: (c) 5


Q27. In inventory planning, extra inventory is unnecessarily carried to the end of the planning period when using one of the following lot size decision policies

(a) Lot-for-lot production 
(b) Economic order quantity (EOQ) lot size 
(c) Period order quantity (POQ) lot size 
(d) Part period total cost balancing                                                     (GATE-ME-1998)

Ans:  (b) Economic order quantity (EOQ) lot size


Q28 If at the optimum in a linear programming problem, a dual variable corresponding to a particular primal constraint is zero, then it means that

(a) right hand side of the primal constraint can be altered without affecting the optimum solution
(b) changing the right hand side of the primal constraint will disturb the optimum solution 
(c) the objective function is unbounded 
(d) the problem is degenerate.                                                            (GATE-ME-1996)

Ans: (a) right hand side of the primal constraint can be altered without affecting the optimum solution


Q29. In the construction of networks, dummy activities are introduced in order to

(a) compute the slack on all events 
(b) transfer resources, if necessary, during monitoring 
(c) clearly designate a precedence relationship 
(d) simplify the crashing plan.                                                                   (GATE-ME-1990)

Ans: (c) clearly designate a precedence relationship


Q30. The expected time (te) of a PERT activity in terms of optimistic time (t0), pessimistic (tp) and most likely time (tL) is given by

\[ \text { (a) } t_{e}=\frac{t_{0}+4 t_{L}+t_{p}}{6}\]


\[\text { (b) } t_{e}=\frac{t_{0}+4 t_{p}+t_{L}}{6} \]


\[\text { (c) } t_{e}=\frac{t_{0}+4 t_{L}+t_{p}}{3} \]


\[ \text { (d) } t_{e}=\frac{t_{0}+4 t_{p}+t_{L}}{3}\] 



Ans:  \[ \text { (a) } t_{e}=\frac{t_{0}+4 t_{L}+t_{p}}{6}\]



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