1
GATE ME 2011
MCQ (Single Correct Answer)
+2
-0.6
One unit of product $${P_1}$$ requires $$3$$ $$kg$$ of resource $${R_1}$$ and $$1$$ $$kg$$ of resource $${R_2}$$. One unit of product $${P_2}$$ requires $$2$$ $$kg$$ of resource $${R_1}$$ and $$2$$ $$kg$$ of resource $${R_2}$$. The profits per unit by selling product $${P_1}$$ and $${P_2}$$ are Rs. $$2000$$ and Rs. $$3000$$ respectively. The manufacturer has $$90$$ $$kg$$ of resource $${R_1}$$ and $$100$$ $$kg$$ of resource $${R_2}$$.

The manufacturer can make a maximum profit of Rs.

A
$$60,000$$
B
$$135,000$$
C
$$150,000$$
D
$$200,000$$
2
GATE ME 2009
MCQ (Single Correct Answer)
+2
-0.6
Consider the following Linear Programming problem $$(LLP)$$

Maximize: $$Z = 3{x_1} + 2{x_2}$$
$$\,\,$$ Subject $$\,\,$$ to
$$\eqalign{ & \,\,\,\,\,\,\,{x_1} \le 4 \cr & \,\,\,\,\,\,\,{x_2} \le 6 \cr & 3{x_1} + 2{x_2} \le 18 \cr & {x_1} \ge 0,\,\,{x_2} \ge 0 \cr} $$

A
The $$LPP$$ has a unique optimal solution.
B
The $$LPP$$ is infeasible
C
The $$LPP$$ is unbounded
D
The $$LPP$$ has multiple optimal solutions.
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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