1

GATE ME 2017 Set 1

Numerical

+2

-0

Two models, $$P$$ and $$Q,$$ of a product earn profits of Rs. $$100$$ and Rs. $$80$$ per piece, respectively. Production times for $$P$$ and $$Q$$ are $$5$$ hours and $$3$$ hours, respectively, while the total production time available is $$150$$ hours. For a total batch size of $$40,$$ to maximize profit, the number of units of $$P$$ to be produced is ____________.

Your input ____

2

GATE ME 2016 Set 1

MCQ (Single Correct Answer)

+2

-0.6

Maximize $$\,\,\,\,Z = 15{x_1} + 20{x_2}$$

Subject to

$$\eqalign{ & 12{x_1} + 4{x_2} \ge 36 \cr & 12{x_1} - 6{x_2} \le 24 \cr & \,\,\,\,\,\,\,\,\,{x_1},\,\,{x_2} \ge 0 \cr} $$

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

3

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. _______________

Your input ____

4

GATE ME 2015 Set 3

MCQ (Single Correct Answer)

+2

-0.6

For the linear programming problem:

$$\eqalign{ & Maximize\,\,\,\,\,Z = 3{x_1} + 2{x_2} \cr & Subject\,\,to\,\,\,\, - 2{x_1} + 3{x_2} \le 9 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{x_1} - 5{x_2} \ge - 20 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{x_1},\,\,{x_2} \ge 0 \cr} $$

$$\eqalign{ & Maximize\,\,\,\,\,Z = 3{x_1} + 2{x_2} \cr & Subject\,\,to\,\,\,\, - 2{x_1} + 3{x_2} \le 9 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{x_1} - 5{x_2} \ge - 20 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{x_1},\,\,{x_2} \ge 0 \cr} $$

The above problem has

Questions Asked from Linear Programming (Marks 2)

Number in Brackets after Paper Indicates No. of Questions

GATE ME Subjects

Engineering Mechanics

Machine Design

Strength of Materials

Heat Transfer

Production Engineering

Industrial Engineering

Turbo Machinery

Theory of Machines

Engineering Mathematics

Fluid Mechanics

Thermodynamics

General Aptitude