1
GATE ME 2005
+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 $${v_2}$$
2
GATE ME 2004
+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
$$1000,1000$$
3
GATE ME 2003
+2
-0.6
A manufacturer produces two types of products, $$1$$ and $$2,$$ at production levels of $${x_1}$$ and $${x_2}$$ respectively. The profit is given is$$2{x_1} + 5{x_2}.$$ The production constraints are \eqalign{ & {x_1} + 3{x_2} \le 40 \cr & 3{x_1} + {x_2} \le 24 \cr & {x_1} + {x_2} \le 10 \cr & {x_1} > 0,\,{x_2} > 0 \cr}\$

The maximum profit which can meet the constraints is

A
$$29$$
B
$$38$$
C
$$44$$
D
$$75$$
GATE ME Subjects
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Medical
NEET