GATE ME
Industrial Engineering
Linear Programming
Previous Years Questions

## Marks 1

Simplex method of solving linear programming problem uses
If at the optimum in a linear programming problem, a dual variable corresponding to a particular primal constraint is zero, then it means that

## Marks 2

Maximize $$\,\,\,\,\,\,\,\,\,Z = 5{x_1} + 3{x_2}$$ Subject to $$\,\,\,\,\,\,\,\,\,\,{x_1} + 2{x_2} \le 10,$$ \eqalign{ & \,\,\,\,\,\,\,\,\,\,... 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$$are... A firm uses a turning center, a milling center and a grinding machine to produce two parts. The table below provides the machining time required for... Maximize$$\,\,\,\,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 &...
For the linear programming problem: \eqalign{ & Maximize\,\,\,\,\,Z = 3{x_1} + 2{x_2} \cr & Subject\,\,to\,\,\,\, - 2{x_1} + 3{x_2} \... Consider an objective functionZ\left( {{x_1},{x_2}} \right) = 3{x_1} + 9{x_2}$$and the constraints$$\eqalign{ & {x_1} + {x_2} \le 8, \cr ...
A linear programming problem is shown below. \eqalign{ & Maximize\,\,\,\,3x + 7y \cr & Subject\,\,to\,\,\,3x + 7y \le 10 \cr &... One unit of product{P_1}$$requires$$3kg$$of resource$${R_1}$$and$$1kg$$of resource$${R_2}$$. One unit of product$${P_2}$$requir... One unit of product$${P_1}$$requires$$3kg$$of resource$${R_1}$$and$$1kg$$of resource$${R_2}$$. One unit of product$${P_2}$$requir... Consider the following Linear Programming problem$$(LLP)$$Maximize:$$Z = 3{x_1} + 2{x_2}\,\,$$Subject$$\,\,$$to$$\eqalign{ & \,\,\,...
Consider the Linear programme $$(LP)$$ Max $$4x$$ + $$6y$$ Subject to \eqalign{ & \,\,\,\,\,\,\,\,\,\,\,3x + 2y \le 6 \cr & \,\,\,\,... Consider the Linear programme(LP)$$Max$$4x$$+$$6y$$Subject to$$\eqalign{ & \,\,\,\,\,\,\,\,\,\,\,3x + 2y \le 6 \cr & \,\,\,\,...
Consider a linear programming problem with two variables and two constraints. The objective function is: Maximize $${x_1} + {x_2}.$$ The corner points...
Consider a linear programming problem with two variables and two constraints. The objective function is: Maximize $${x_1} + {x_2}.$$ The corner points...
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 ...
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$... ## Marks 5 A furniture manufacturer produces chairs and tables. The wood-working department is capable of producing $$200$$ chairs or $$100$$ tables or any propo... Solve the following linear programming problem by simplex method$\$\eqalign{ & Maximize\,\,\,\,\,\,4{x_1} + 6{x_2} + {x_3} \cr & Subjec...
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