1
GATE ME 2002
MCQ (Single Correct Answer)
+2
-0.6
Arrivals at a telephone booth are considered to be Poisson, with an average time of $$10$$ minutes between successive arrivals. The length of a phone call is distributed exponentially with mean $$3$$ minutes. The probability that an arrival does not have to wait before service is
A
$$0.3$$
B
$$0.5$$
C
$$0.7$$
D
$$0.9$$
2
GATE ME 2002
Subjective
+5
-0
A furniture manufacturer produces chairs and tables. The wood-working department is capable of producing $$200$$ chairs or $$100$$ tables or any proportionate combinations of these per week. The weekly demand for chairs and tables is limited to $$150$$ and $$80$$ units respectively. The profit from a chair is Rs.$$100$$ and that from a table is Rs.$$300.$$

$$(a)$$ Set up the problem as a Linear Program
$$(b)$$ Determine the optimum product mix for maximizing the profit.
$$(c)$$ What is the maximum profit?
$$(d)$$ If the profit of each table drops to Rs.200 per unit, what is the optimal mix and profit?

3
GATE ME 2002
MCQ (Single Correct Answer)
+2
-0.6
The supply at three sources is $$50, 40$$ and $$60$$ units respectively whilst the demand at the four destinations is $$20, 30, 10$$ and $$50$$ units. In solving this transportation problem
A
a dummy source of capacity $$40$$ units is needed
B
a dummy destination of capacity $$40$$ units is needed
C
no solution exists as the problem is infeasible
D
none solution exists as the problem is degenerate
4
GATE ME 2002
MCQ (Single Correct Answer)
+1
-0.3
A static load is mounted at the center of a shaft rotating at uniform angular velocity. This shaft will be designed for
A
the maximum compressive stress (static)
B
the maximum tensile (static)
C
the maximum bending moment (static)
D
fatigue loading
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