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Questions Related to business maths

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

Show answer
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

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  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

Show answer
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.

In transportation models designed in linear programming, points of demand is classified as

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

  1. ordination

  2. transportation

  3. destinations

  4. origins

Show answer
Correct Option: C
Explanation:

In linear programming, transportation modeltransportation model are applied to problems related to the study of efficient transportation routes. i.e., how effectively the available resources are transported to different destinations with minimum cost.

Therefore, the points of demand is classified as destinations.

Consider the following linear programming problem:

Maximize $12X + 10Y$
Subject to: $4X + 3Y ≤ 480$
  $2X + 3Y ≤ 360$
  all variables $ ≥0$

Which of the following points $(X,Y)$ could be a feasible corner point?

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

  1. $(40,48)$

  2. $(120,0)$

  3. $(180,120)$

  4. $(30,36)$

  5. None of these

Show answer
Correct Option: B
Explanation:

Given constraints, $4x+3y\leq 480$ and $2x+3y\leq 360$


first, draw the graph for equations $4x+3y= 480$ and $2x+3y= 360$

for $4x+3y= 480$
substitute y=0 we get, $4x=480 \implies x=120$
substitute x=0 we get, $3y=480 \implies y=160$
therefore, $4x+3y= 480$ line passes through (120,0) and (0,160) as shown in fig.
Hence, $4x+3y\leq 480$ includes the region below the line.


for $2x+3y= 360$
substitute y=0 we get, $2x=360 \implies x=180$
substitute x=0 we get, $3y=360 \implies y=120$
therefore, $4x+3y= 480$ line passes through $(180,0)$ and $(0,120)$ as shown in fig.
Hence, $2x+3y\leq 360$ includes the region below the line.

the shaded region as shown in figure is intersection region. From the figure, $(0,120)$ and $(120,0)$ are feasible corner points.

Consider the following linear programming problem:

Maximize $12X + 10Y$
Subject to: $4X + 3Y ≤ 480$
  $2X + 3Y ≤ 360$
all variables $ ≥0$

Which of the following points $(X,Y)$ is feasible?

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

  1. $(10,120)$

  2. $(120,10)$

  3. $(30,100)$

  4. $(60,90)$

  5. None of the above

Show answer
Correct Option: C
Explanation:

Consider point $(10,120)$ , It doesnt satisfy the inequality $2X+3Y \le 360$

Consider point $(120,10)$ , it doesnt satisfy the inequality $4X+3Y \le 480$
Consider point $(30,100)$ , it satisfies all the inequalities . So this point is feasible
Consider point $(60,90)$ , it doesnt satisfies the inequalities $2X+3Y \le 360$ and $4X+3Y \le 480$
Therefore the correct option is $C$

Unboundedness is usually a sign that the LP problem.

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

  1. has finite multiple solutions.

  2. is degenerate.

  3. contains too many redundant constraints.

  4. has been formulated improperly.

  5. none of the above.

Show answer
Correct Option: D
Explanation:

A linear programming problem is said to have unbounded solution if it has infinite number of solutions. I.e., the problem has been formulated improperly

The first step in formulating an LP problem is

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

  1. graph the problem.

  2. perform a sensitivity analysis.

  3. identify the objective and the constraints.

  4. define the decision variables.

  5. understand the managerial problem being faced.

Show answer
Correct Option: E
Explanation:

The first step in formulating an linear programming problem is to understand the managerial problem being faced i.e., determine the quantities that are needed to solve the problem.