1
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 $$0$$).

After some simplex iterations, the following table is obtained

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
2
GATE ME 2005
MCQ (Single Correct Answer)
+2
-0.6
Consider a linear programming problem with two variables and two constraints. The objective function is: Maximize $${x_1} + {x_2}.$$ The corner points of the feasible region are $$(0,0), (0,2), (2,0)$$ and $$(4/3, 4/3).$$

If an additional constraint $${x_1} + {x_2} \le 5$$ is added, the optimal solution is

A
$$\left( {{5 \over 3},{5 \over 3}} \right)$$
B
$$\left( {{4 \over 3},{4 \over 3}} \right)$$
C
$$\left( {{5 \over 2},{5 \over 2}} \right)$$
D
$$(5,0)$$
3
GATE ME 2005
MCQ (Single Correct Answer)
+2
-0.6
Consider a linear programming problem with two variables and two constraints. The objective function is: Maximize $${x_1} + {x_2}.$$ The corner points of the feasible region are $$(0,0), (0,2), (2,0)$$ and $$(4/3, 4/3).$$

Let $${y_1}$$ and $${y_2}$$ be the decision variables of the dual and $${v_1}$$ and $${v_2}$$ be the slack variables of the dual of the given linear programming problem. The optimum dual variables are

A
$${y_1}$$ and $${y_2}$$
B
$${y_1}$$ and $${v_1}$$
C
$${y_1}$$ and $${v_2}$$
D
$${v_1}$$ and $${v_2}$$
4
GATE ME 2004
MCQ (Single Correct Answer)
+2
-0.6
A company produces two types of toys: $$P$$ and $$Q.$$ Production time of $$Q$$ is twice that of $$P$$ and the company has a maximum of $$2000$$ time units per day. The supply of raw material is just sufficient to produce $$1500$$ toys (of any type) per day. Toy type $$Q$$ requires an electric switch which is available @ $$600$$ pieces per day only. The company makes a profit of Rs.$$3$$ and Rs.$$5$$ on type $$P$$ and $$Q$$ respectively. For maximization of profits, the daily production quantities of $$P$$ and $$Q$$ toys should respectively be
A
$$100, 500$$
B
$$500,1000$$
C
$$800,600$$
D
$$1000,1000$$
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