1
GATE ME 2016 Set 3
Numerical
+2
-0
A firm uses a turning center, a milling center and a grinding machine to produce two parts. The table below provides the machining time required for each part and the maximum machining time available on each machine. The profit per unit on parts $${\rm I}$$ and $${\rm II}$$ are Rs. $$40$$ and Rs. $$100,$$ respectively. The maximum profit per week of the firm is Rs. _______________
2
GATE ME 2016 Set 1
+2
-0.6
Maximize $$\,\,\,\,Z = 15{x_1} + 20{x_2}$$
Subject to
\eqalign{ & 12{x_1} + 4{x_2} \ge 36 \cr & 12{x_1} - 6{x_2} \le 24 \cr & \,\,\,\,\,\,\,\,\,{x_1},\,\,{x_2} \ge 0 \cr}

The above linear programming problem has

A
infeasible solution
B
unbounded solution
C
alternative optimum solutions
D
degenerate solution
3
GATE ME 2015 Set 3
+2
-0.6
For the linear programming problem:
\eqalign{ & Maximize\,\,\,\,\,Z = 3{x_1} + 2{x_2} \cr & Subject\,\,to\,\,\,\, - 2{x_1} + 3{x_2} \le 9 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{x_1} - 5{x_2} \ge - 20 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{x_1},\,\,{x_2} \ge 0 \cr}

The above problem has

A
Unbounded solution
B
Infeasible solution
C
Alternative optimum solution
D
Degenerate solution
4
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 ________________.