Tag: structure of linear programming model

Questions Related to structure of linear programming model

The given table shows the number of cars manufactured in four different colours on a particular day. Study it carefully and answer the question.

 Colour    Number of cars manufactured
 Vento  Creta
 Red  65
 White  54
 Black  66
 Sliver 37

What was the total number of black cars manufactured?

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

  1. $240$

  2. $206$

  3. $205$

  4. $159$

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Correct Option: B
Explanation:

The number of Black cars manufactured 


$=$ no. of black $Vento$ +no. of black $Creta$ +no. of black $WagonR$ 

$=66+52+88 =206$          

" the relation S is defined on $N\times N\left ( a,b \right )S\left ( c,d \right )\Leftrightarrow bc\left ( a+d \right )=ad$ in an equivalance " that statement is ?

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

  1. True

  2. False

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Correct Option: A

If a = b then ax = ...........

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

  1. $b + x$

  2. bx

  3. b - x

  4. $b\, \div\, x$

Show answer
Correct Option: B
Explanation:

Given,

a = b
Multiplying both sides by x.
ax = bx

If  x + y = 3 and xy = 2, then the value of $\displaystyle x^{3}-y^{3}$ is equal to 

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

  1. 6

  2. 7

  3. 8

  4. 0

Show answer
Correct Option: B
Explanation:

Formula used:
$x^3-y^3=(x-y)(x^2+xy+y^2)$
               $=(\sqrt{(x+y)^2-4xy})[(x+y)^2-xy]$
               $=(\sqrt{(3)^2-4(2)})[(3)^2-2]$
               $=(\sqrt 1)(7)=7$
Option B is correct.

What is the solution of $x\le 4,y\ge 0$ and $x\le -4,y\le 0$ ?

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

  1. $x\ge -4,y\le 0$

  2. $x\le 4,y\ge 0$

  3. $x\le -4,y=0$

  4. $x\ge -4,y=0$

Show answer
Correct Option: C
Explanation:

$x \le 4$ and $x \le -4$

$\Rightarrow x \le -4$
Also,
$y \ge 0$ and $y \le 0$
$\Rightarrow y = 0$
Hence the solutione is $x \le -4, \; y = 0$.

Solving an integer programming problem by rounding off answers obtained by solving it as a linear programming problem (using simplex), we find that

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

  1. The values of decision variables obtained by rounding off are always very close to the optimal values.

  2. The value of the objective function for a maximization problem will likely be less than that for the simplex solution.

  3. The value of the objective function for a minimization problem will likely be less than that for the simplex solution.

  4. All constraints are satisfied exactly.

  5. None of the above.

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Correct Option: B
Explanation:

Solving an integer programming problem by rounding off answers obtained by solving it as a linear programming problem, we find that the value of the objective function for a maximization problem will likely be less than that for the simplex solution.

If the constraints in linear programming problem are changed

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

  1. the problem is to be re-evaluated

  2. solution is not defined

  3. the objective function has to be modified

  4. the change in constraints is ignored

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Correct Option: A
Explanation:

The above question asks for the impact of change in constraints on the Linear programming problem. In this scenario, when there is a change in constraint, the solution will change definitely. Whether the solution exists or not, we can only find once the problem is re-evaluated. 

In an LPP, the objective function is related to the main objective of any problem, either we have to maximize or minimize the function based on the situation whereas the constraints is related to physical restrictions in achieving the defined objective function. In real life problems, there might be situations when the constraints change, but objective function does not changes to accommodate the change in constraints.
Thus, if constraints in linear programming problem is changed, the problem has to be re-evaluated for the same objective function and after solving we can find whether the solution exists or not.

A wholesale merchant wants to start the business of cereal with Rs. $24000$. Wheat is Rs. $400$ per quintal and rice is Rs. $600$ per quintal. He has capacity to store $200$ quintal cereal. He earns the profit Rs.$25$ per quintal on wheat and Rs. $40$ per quintal on rice. If he stores $x$ quintal rice and $y$ quintal wheat, then for maximum profit the objective function is

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

  1. $25x+40y$

  2. $40x+25y$

  3. $400x+600y$

  4. $\dfrac{400}{40}x + \dfrac{600}{25}y$

Show answer
Correct Option: B

The given table shows the number of cars manufactured in four different colours on a particular day. Study it carefully and answer the question.

 Colour    Number of cars manufactured
 Vento  Creta
 Red  65
 White  54
 Black  66
 Sliver 37

Which car was twice the number of silver Vento?

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

  1. Silver WagonR

  2. Red WagonR

  3. Red Vento

  4. White Creta

Show answer
Correct Option: A
Explanation:

The number of silver Vento car $=37$  (from the table)


Twice the number of silver Vento cars$ = 2 \times 37=74$

Now from table we can see that silver WagonR is only car type having $74 $ cars  

The feasible solution of an LP problem, is ________

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

  1. must satisfies all of the problem's constraints simultaneously

  2. must be a corner point of the feasible region

  3. need not satisfy all of the constraints, only some of them

  4. must optimize the value of the objective function

Show answer
Correct Option: A
Explanation:

the feasibe solution of a inear programming probem(LP) is a solution that must satisfy all of the problem's constraints simultaniously