Tag: structure of linear programming model

Questions Related to structure of linear programming model

The solution of the set of constraints of a linear programming problem is a convex (open or closed) is called ______ region.

business maths linear programming problems structure of linear programming model linear programming problem operations research

  1. feasible

  2. active

  3. linear

  4. none of these

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Correct Option: A

Let $P(-1, 0), Q(0, 0)$ and $R(3, 3\sqrt{3})$ be three points. The equation of the bisector of the angle PQR is?

business maths linear programming problems structure of linear programming model linear programming problem operations research

  1. $x+\sqrt{3}y=0$

  2. $\sqrt{3}x+y=0$

  3. $x+\dfrac{\sqrt{3}}{2}y=0$

  4. $\dfrac{\sqrt{3}}{2}x+y=0$

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Correct Option: B

Maximum value of $z = 6 x + 11 y$ ,  subject to $2 x + y \leq 104 , x + 2 y \leq 76 , x \geq 0 , y \geq 0$ is

business maths linear programming problems structure of linear programming model linear programming problem operations research

  1. $240$

  2. $540$

  3. $440$

  4. $410$

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Correct Option: A

The taxi fare in a city is as follows. For the first km the fare is $Rs.10$ and subsequent distance is $Rs.6 / km.$ Taking the distance covered as $x \ km$ and fare as $Rs\ y$ ,write a linear equation.

business maths linear programming problems structure of linear programming model linear programming problem operations research

  1. $y=4+6x$

  2. $y=4+5x$

  3. $y=3+6x$

  4. $y=3+5x$

Show answer
Correct Option: A
Explanation:

First $km$ fare =$Rs.10$

Subsequent distance fare=$Rs\ 6/km$

Then fare $x\ km$ of distance 
$y=(x-1) \times 6+10$
$y=6x-6+10$

$y=6x+4$

$A$ is correct 



The problem associated with  $ LPP$  is

business maths linear programming problems structure of linear programming model linear programming problem operations research

  1. single objective function

  2. Double objective function

  3. No any objective function

  4. None

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Correct Option: A
Explanation:

The problem associated with LLP is single objective.

A train travelling at 48 kmph completely crosses another train having half its length and travelling in opposite direction at 42 kmph in 12 seconds. It also passes a railway platform in 45 seconds. The length of the platform is

business maths linear programming problems structure of linear programming model linear programming problem operations research

  1. $400 m$

  2. $200 m$

  3. $600 m$

  4. $250 m$

Show answer
Correct Option: A
Explanation:

Let the length of the first train be $x$ metres


length of the second train$=\dfrac{x}{2}$m


relative speed of the two trains$=48+42$

                                                    $=90kmph$

                                                    $=90\times\dfrac{5}{18}$

                                                    $=25m/s$

$25=\dfrac{x+\dfrac{x}{2}}{12}$

$25=\dfrac{2x+x}{24}$

$3x=25\times24$

$x=25\times8$

$x=200$

So, the length of the train $=200m$

Let the length of the platform be y

Speed of the train $=48 kmph$

                                 $=48\times\dfrac{5}{18}$

                                  $=\dfrac{40}{3}m/s$

$\dfrac{40}{3}=\dfrac{200+y}{45}$

$40\times45=600+3y$

$1800=600+3y$

$3y=1200$

$y=400$

So, the length of the platform$=400m$


Linear programming used to optimize mathematical procedure and is

business maths linear programming problems structure of linear programming model linear programming problem operations research

  1. subset of mathematical programming

  2. dimension of mathematical programming

  3. linear mathematical programming

  4. all of above

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Correct Option: A
Explanation:

Linear programming is an extremely powerful tool for addressing a wide range of applied optimization problems. A short list of application areas is resource allocation, production scheduling, warehousing, layout, transportation scheduling, facility location, flight crew scheduling, portfolio optimization, parameter estimation.
So ,linear programming is used to subset mathematical programming.

In linear programming, oil companies used to implement resources available is classified as

business maths linear programming problems structure of linear programming model linear programming problem operations research

  1. implementation modeling

  2. transportation models

  3. oil model

  4. resources modeling

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Correct Option: B
Explanation:

In linear programming, $\text{transportation model}$ are applied to problems related to the study of efficient transportation routes.

For oil companies, how effectively the available resources are transported to different destinations with minimum cost.

Linear programming model which involves funds allocation of limited investment is classified as

business maths linear programming problems structure of linear programming model linear programming problem operations research

  1. ordination budgeting model

  2. capital budgeting models

  3. funds investment models

  4. funds origin models

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Correct Option: B
Explanation:
In linear programming, $\text{Capital budgeting models}$ to minimize the total capital cost. 
The solutions from the model are used to decide the best combination of capital resources and best times to start and finish projects and to determine the net capital cost.

Which of the following is a property of all linear programming problems?

business maths linear programming problems structure of linear programming model linear programming problem operations research

  1. alternate courses of action to choose from

  2. minimization of some objective

  3. a computer program

  4. usage of graphs in the solution

  5. usage of linear and nonlinear equations and inequalities

Show answer
Correct Option: A
Explanation:
According to Robbins, the resources(capital, land, labour, materials, ...) are always limited. Every resource have multiple uses.

The problem before any organisation or manager is to choose the best alternatives which can maximize the profit or minimize the cost of production. Linear programming is the method which is used to select the best possible alternatives from the all alternatives.

According to William M. Fox, "Linear programming is a planning technique that permits some objective function to be maximized or minimized within the framework of given situational restrictions"

Therefore, the linear programming is the process of selecting best courses of action to choose from various alternatives.