1
GATE ME 2008
MCQ (Single Correct Answer)
+2
-0.6
A moving average system is used for forecasting weekly demand. $${F_1}\left( t \right)$$ and $${F_2}\left( t \right)$$ are sequences of forecasts with parameters $${m_1}$$ and $${m_2}$$, respectively, where $${m_1}$$ and $${m_2}\left( {{m_1} > {m_2}} \right)$$ denote the numbers of weeks over which the moving averages are taken. The actual demand shows a step increase from $${d_1}$$ to $${d_2}$$ at a certain time. Subsequently,
A
neither $${F_1}\left( t \right)$$ nor $${F_2}\left( t \right)$$ will catch up with the value $${d_2}$$
B
both sequences $${F_1}\left( t \right)$$ and $${F_2}\left( t \right)$$ will reach $${d_2}$$ in the same period
C
$${F_1}\left( t \right)$$ will attain the value $${d_2}$$
D
$${F_2}\left( t \right)$$ will attain the value $${d_2}$$
2
GATE ME 2008
MCQ (Single Correct Answer)
+1
-0.3
In an $$M/M/1$$ queuing system, the number of arrivals in an interval of length $$T$$ is a Poisson random variable (i.e., the probability of there being $$n$$ arrivals in an interval of length $$T$$ is $${{{e^{ - \lambda T}}{{\left( {\lambda T} \right)}^n}} \over {n!}}$$). The probability density function $$f(t)$$ of the inter-arrival time is given by
A
$${\lambda ^2}\left( {{e^{ - {\lambda ^2}t}}} \right)$$
B
$$\left( {{{{e^{ - {\lambda ^2}t}}} \over {{\lambda ^2}}}} \right)$$
C
$$\lambda {e^{ - \lambda t}}$$
D
$${{{{e^{ - \lambda t}}} \over \lambda }}$$
3
GATE ME 2008
MCQ (Single Correct Answer)
+2
-0.6
Consider the Linear programme $$(LP)$$
Max $$4x$$ + $$6y$$
Subject to
$$\eqalign{ & \,\,\,\,\,\,\,\,\,\,\,3x + 2y \le 6 \cr & \,\,\,\,\,\,\,\,\,\,\,2x + 3y \le 6 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x,y \ge 0 \cr} $$

The dual for the $$LP$$ is

A
$$\eqalign{ & {Z_{\min }} = 6u + 6v \cr & \,\,subjuect\,\,to\,\, \cr & 3u + 2v \ge 4 \cr & 2u + 3v \ge 6 \cr & u,v \ge 0 \cr} $$
B
$$\eqalign{ & {Z_{\max }} = 6u + 6v \cr & \,\,subjuect\,\,to\,\, \cr & 3u + 2v \le 4 \cr & 2u + 3v \le 6 \cr & u,v \ge 0 \cr} $$
C
$$\eqalign{ & {Z_{\max }} = 4u + 6v \cr & \,\,subjuect\,\,to\,\, \cr & 3u + 2v \ge 6 \cr & 2u + 3v \ge 6 \cr & u,v \ge 0 \cr} $$
D
$$\eqalign{ & {Z_{\max }} = 4u + 6v \cr & \,\,subjuect\,\,to\,\, \cr & 3u + 2v \le 6 \cr & 2u + 3v \le 6 \cr & u,v \ge 0 \cr} $$
4
GATE ME 2008
MCQ (Single Correct Answer)
+2
-0.6
Consider the Linear programme $$(LP)$$
Max $$4x$$ + $$6y$$
Subject to
$$\eqalign{ & \,\,\,\,\,\,\,\,\,\,\,3x + 2y \le 6 \cr & \,\,\,\,\,\,\,\,\,\,\,2x + 3y \le 6 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x,y \ge 0 \cr} $$

After introducing slack variables $$s$$ and $$t$$, the initial basic feasible solution is represented by the table below (basic variables are $$s=6$$ $$t=6,$$ and the objective function value is $$0$$).
GATE ME 2008 Industrial Engineering - Linear Programming Question 14 English 1

After some simplex iterations, the following table is obtained
GATE ME 2008 Industrial Engineering - Linear Programming Question 14 English 2
From this, one can conclude that

A
The $$LP$$ has a unique optimal solution
B
The $$LP$$ has an optimal solution that is not unique
C
The $$LP$$ is infeasible
D
The $$LP$$ is unbounded
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