1

GATE ME 2002

Subjective

+5

-0

A furniture manufacturer produces chairs and tables. The wood-working department is capable of producing $$200$$ chairs or $$100$$ tables or any proportionate combinations of these per week. The weekly demand for chairs and tables is limited to $$150$$ and $$80$$ units respectively. The profit from a chair is Rs.$$100$$ and that from a table is Rs.$$300.$$

$$(a)$$ Set up the problem as a Linear Program

$$(b)$$ Determine the optimum product mix for maximizing the profit.

$$(c)$$ What is the maximum profit?

$$(d)$$ If the profit of each table drops to Rs.200 per unit, what is the optimal mix and profit?

2

GATE ME 2000

Subjective

+5

-0

Solve the following linear programming problem by simplex method

$$\eqalign{ & Maximize\,\,\,\,\,\,4{x_1} + 6{x_2} + {x_3} \cr & Subject\,\,to\,\,\,\,\,\,2{x_1} - {x_2} + 3{x_3}\, \le 5 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{x_1},{x_2},{x_3} \ge 0 \cr} $$

$$(a)$$$$\,\,\,\,\,\,\,$$ What is the solution to the above problem?

$$(b)$$$$\,\,\,\,\,\,\,$$ Add the constant $${x_2} \le 2$$ to the simplex table of part $$(a)$$ and find the solution.

Questions Asked from Linear Programming (Marks 5)

Number in Brackets after Paper Indicates No. of Questions

GATE ME Subjects

Engineering Mechanics

Strength of Materials

Theory of Machines

Engineering Mathematics

Machine Design

Fluid Mechanics

Turbo Machinery

Heat Transfer

Thermodynamics

Production Engineering

Industrial Engineering

General Aptitude