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GATE Past Year Questions: Linear Programming | Industrial Engineering - Mechanical Engineering PDF Download

Question for GATE Past Year Questions: Linear Programming
Try yourself:The manufacturer can make a maximum profit of  Rs.

[2011]

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Question for GATE Past Year Questions: Linear Programming
Try yourself: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 units per day. The supply of raw material is just sufficient to produce 1500 toys (of any type) per day. Toy type Q requires an electric switch which is available @ 600 pieces per day only.The company makes a profit of Rs. 3 and Rs. 5 on type P and Q respectively. For maximization​of profits, the daily production quantities of P and Q toys should respectively be

[2004]

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Question for GATE Past Year Questions: Linear Programming
Try yourself: Simplex method of solving linear programming problem uses

[2010]

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Question for GATE Past Year Questions: Linear Programming
Try yourself:The dual for the LP in Q. 21 is

[2008]

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Question for GATE Past Year Questions: Linear Programming
Try yourself:After introducing slack variables s and t, the initial basic feasible solution is represented by the table below (basic variables are s = 6 and t = 6, and the objective function value is 0).
GATE Past Year Questions: Linear Programming | Industrial Engineering - Mechanical Engineering
After some simplex iterations, the following table is obtained
GATE Past Year Questions: Linear Programming | Industrial Engineering - Mechanical Engineering
From this, one can conclude that

[2008]

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Question for GATE Past Year Questions: Linear Programming
Try yourself:For the standard transportation linear program with m sources and n destinations and total supply equaling total demand, an optimal solution (lowest cost) with the smallest number of non-zero xij values (amounts from source i to destination j) is desired. The best upper bound for this number is

[2008]

 

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Question for GATE Past Year Questions: Linear Programming
Try yourself:For the linear programming problem:
Maximize z = 3x1 + 2x2
Subject to –2x1 + 3x2 < 9x1 – 5x2 > – 20x1, x2 > 0
The above problem has

[2016]

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Question for GATE Past Year Questions: Linear Programming
Try yourself:Maximize z = 15x1 + 20x2
Subject to 12x1 + 4x2 >  36
12x1 + 6x2 > 24 x1,
x2 > 0
The above linear programming problem has
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Question for GATE Past Year Questions: Linear Programming
Try yourself:A linear programming problem is shown below:
Maximise 3x + 7y
Subjeot to 3x + 7y < 10
4x + 6y < 8 x, y > 0

[2013]

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Question for GATE Past Year Questions: Linear Programming
Try yourself:The manufacturer can make a maximum profit of  Rs.

[2011]

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Question for GATE Past Year Questions: Linear Programming
Try yourself:One unit of product P1 requires 3 kg of resource R1 and 1 kg resource R2. One unit of product P2 requires 2 kg of resource R1 and 2 kg of resource R2. The profits per unit by selling product P1 and P2 and Rs. 12000 and Rs 3000 respectively. The manufacturer has 90 kg of resource R1, and 100 kg of resource R2.

The unit worth of resource R2, i.e. dual price of resource R2 in Rs per kg is

[2011]

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Question for GATE Past Year Questions: Linear Programming
Try yourself:Consider the following Linear Programming Problem (LPP):
Maximize z = 3x1 + 2x2,
Subject to x1 < 4 x2 < = 6
3x1 + 2x2 < 18
x1 > 0, x2 > 0

[2009]

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Question for GATE Past Year Questions: Linear Programming
Try yourself:A firm is required to procure three items (P, Q, and R). The prices quoted for these items (in Rs.) by suppliers S1,  S2 and S3 are given in table. The management policy requires that each item has to be supplied by only one supplier and one supplier supply only one item.The minimum total cost (in Rs.) of procurement to the firm is

[2006]

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Question for GATE Past Year Questions: Linear Programming
Try yourself:Let Y1 and Y2 be the decision variables of the dual and v1 and v2 be the slack variables of the dual of the given linear programming problem.The optimum dual variables are

[2005]

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Question for GATE Past Year Questions: Linear Programming
Try yourself:If an additional constraint X1 + X2 < 5 is added, the optimal solution is

[2005]

 

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Question for GATE Past Year Questions: Linear Programming
Try yourself:A company has two factories S1, S2 and two warehouses D1, D2. The supplies from S1 and S2 are 50 and 40 units respectively. Warehouse D1 requires a minimum of 20 units and a maximum of 40 units. Warehouse D2 requires a minimum of 20 units and, over and above, it can take as much as can be supplied. A balanced transportation problem is to be formulated for the above situation. The number of supply points, the number of demand points, and the total supply (or total demand) in the balanced transportation problem respectively are

[2005]

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Question for GATE Past Year Questions: Linear Programming
Try yourself:A component can be produced by any of the four processes, I, II, III and IV. Process I has fixed cost of Rs. 20 and variable cost of Rs. 3 per piece.Process II has a fixed cost of Rs. 50 and variable cost of Rs. 1 per piece. Process III has a fixed cost of Rs. 40.00 and variable cost of Rs. 2 per piece. Process IV has fixed cost of Rs. 10 and Variable cost Rs. 4 per piece. If company wishes to produce 100 pieces of the component, from economic point of view it should choose

[2005 : 2 Marks]

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Question for GATE Past Year Questions: Linear Programming
Try yourself:A manufacturer produces two types of products, 1 and 2, at production levels of x1 and x2 respectively. The profit is given is 2x1 + 5x2. The production constraints are:
x1 + 3x2 < 40
3x1 + x2 < 24
x1 + x2 < 10
x1 > 0 x2 > 0
The maximum profit which can meet the constraints is

[2003]

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Question for GATE Past Year Questions: Linear Programming
Try yourself:If at the optimum in a linear programming problem, a dual variable corresponding to a particular primal constraint is zero, then it means that

[1996]

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Question for GATE Past Year Questions: Linear Programming
Try yourself:In an assembly line for assembling toys, five workers are assigned tasks which take times of 10, 8, 6, 9 and 10 minutes respectively. The balance delay for line is

[1996]

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FAQs on GATE Past Year Questions: Linear Programming - Industrial Engineering - Mechanical Engineering

1. What is linear programming in mechanical engineering?
Ans. Linear programming is a mathematical technique used in mechanical engineering to optimize a system with linear constraints. It involves formulating an objective function and a set of constraints, and finding the values that maximize or minimize the objective function while satisfying the constraints.
2. How is linear programming used in mechanical engineering design?
Ans. Linear programming is used in mechanical engineering design to optimize various parameters of a system. It helps in determining the optimal design parameters, such as dimensions, material properties, and operating conditions, by considering multiple constraints and objectives, such as cost minimization, weight reduction, or performance improvement.
3. What are the advantages of using linear programming in mechanical engineering?
Ans. Linear programming offers several advantages in mechanical engineering. It allows engineers to make informed decisions by considering multiple constraints and objectives simultaneously. It helps in optimizing system design, resource allocation, and scheduling. Additionally, it provides a quantitative and mathematical approach to problem-solving, leading to efficient and effective solutions.
4. Can linear programming be used for non-linear problems in mechanical engineering?
Ans. No, linear programming is specifically designed for solving linear optimization problems. It assumes that the relationship between variables is linear, and the objective function and constraints are linear equations or inequalities. For non-linear problems in mechanical engineering, other optimization techniques, such as non-linear programming or evolutionary algorithms, are more appropriate.
5. What are some real-world applications of linear programming in mechanical engineering?
Ans. Linear programming finds various applications in mechanical engineering, including production planning, facility layout design, inventory management, supply chain optimization, and resource allocation. It is also used in vehicle routing, project scheduling, and production line balancing. These applications help in improving efficiency, reducing costs, and optimizing the overall performance of mechanical systems.
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Document Description: GATE Past Year Questions: Linear Programming for Mechanical Engineering 2024 is part of Industrial Engineering preparation. The notes and questions for GATE Past Year Questions: Linear Programming have been prepared according to the Mechanical Engineering exam syllabus. Information about GATE Past Year Questions: Linear Programming covers topics like and GATE Past Year Questions: Linear Programming Example, for Mechanical Engineering 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for GATE Past Year Questions: Linear Programming.
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