1
GATE ME 2014 Set 3
Numerical
+2
-0
Consider an objective function $$Z\left( {{x_1},{x_2}} \right) = 3{x_1} + 9{x_2}$$ and the constraints
$$\eqalign{ & {x_1} + {x_2} \le 8, \cr & {x_1} + 2{x_2} \le 4, \cr & {x_1} \ge 0,{x_2} \ge 0, \cr} $$

The maximum value of the objective function is ________________.

Your input ____
2
GATE ME 2013
MCQ (Single Correct Answer)
+2
-0.6
A linear programming problem is shown below.
$$\eqalign{ & Maximize\,\,\,\,3x + 7y \cr & Subject\,\,to\,\,\,3x + 7y \le 10 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,4x + 6y \le 8 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x,\,\,y \ge 0 \cr} $$

It has ..............

A
an unbounded objective function
B
exactly one optimal solution
C
exactly two optimal solutions
D
infinitely many optimal solutions
3
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 unit worth of resource $${R_2}$$. i.e. dual price of resource $${R_2}$$ in Rs. per $$kg$$ is

A
$$0$$
B
$$1350$$
C
$$1500$$
D
$$2000$$
4
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
$$200,000$$
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