A level Linear Programming Quiz 1

16 Questions

Quiz Description

In this exciting mathematics quiz, we will be looking at linear programming. Linear programming in mathematics mainly deals with looking for solutions to linear equations and/or functions. It is very essential in the provision of optimal solutions to problems with given impediments. Because of this, linear programming is being applied in the business world and many other areas.

Linear programming is a mathematical modeling technique in which a function is maximized or minimized when exposed to several impediments. In simple terms, it is a method used to achieve optimal end results in a mathematical model whose requirements are represented by the use of linear relationships. It can be applied in numerous fields of study such as mathematics, economics, engineering, and business. Some of the industries making use of linear programming are telecommunications, transportation, energy, and manufacturing. Also, it has been found out that linear programming has proven useful in the modeling of diversified problems in scheduling, planning, routing, design, etc Though with all the useful things that can be done with linear programming, it has its limitations. When solving a linear programming model, there is no assurance that we will get integer-valued solutions.

It is important that we have a recap of the topic so that you can be reminded about what’s coming. Now that it has been done, you can go ahead and start answering the quiz. Good luck to you. 

1:

Z = 20x1 + 20x2, subject to x1 ≥ 0, x2 ≥ 0, x1 + 2x2 ≥ 8, 3x1 + 2x2 ≥ 15, 5x1 + 2x2 ≥ 20. The minimum value of Z occurs at


Correct
  • 1:
    (8 , 0)
  • 2:
    (5/2 , 15/4)
  • 3:
    (7/2 , 9/4)
  • 4:
    (0, 10)
2:

Z = 7x + y, subject to 5x + y ≥ 5, x + y ≥ 3, x ≥ 0, y ≥ 0. The minimum value of Z occurs at


Correct
  • 1:
    (3, 0)
  • 2:
    (1/2 , 5/2)
  • 3:
    (7, 0)
  • 4:
    (0, 5)
3:

Minimize Z = 20x1 + 9x2, subject to x1 ≥ 0, x2 ≥ 0, 2x1 + 2x2 ≥ 36, 6x1 + x2 ≥ 60.


Correct
  • 1:
    360 at (18, 0)
  • 2:
    336 at (6, 4)
  • 3:
    540 at (0, 60)
  • 4:
    0 at (0, 0)
4:

Z = 8x + 10y, subject to 2x + y ≥ 1, 2x + 3y ≥ 15, y ≥ 2, x ≥ 0, y ≥ 0. The minimum value of Z occurs at


Correct
  • 1:
    (4.5, 2)
  • 2:
    (1.5, 4)
  • 3:
    (0, 7)
  • 4:
    (7, 0)
5:

Z = 4x1 + 5x2, subject to 2x1 + x2 ≥ 7, 2x1 + 3x2 ≤ 15, x2 ≤ 3, x1, x2 ≥ 0. The minimum value of Z occurs at


Correct
  • 1:
    (3.5, 0)
  • 2:
    (3, 3)
  • 3:
    (7.5, 0)
  • 4:
    (2, 3)
6:

The maximum value of f = 4x + 3y subject to constraints x ≥ 0, y ≥ 0, 2x + 3y ≤ 18; x + y ≥ 10 is


Correct
  • 1:
    35
  • 2:
    36
  • 3:
    34
  • 4:
    none of these
7:

Objective function of a L.P.P. is


Correct
  • 1:
    a constant
  • 2:
    a function to be optimised
  • 3:
    a relation between the variables
  • 4:
    none of these
8:

The optimal value of the objective function is attained at the points


Correct
  • 1:
    on X-axis
  • 2:
    on Y-axis
  • 3:
    which are comer points of the feascible region
  • 4:
    none of these
9:

Region represented by x ≥ 0, y ≥ 0 is


Correct
  • 1:
    first quadrant
  • 2:
    second quadrant
  • 3:
    third quadrant
  • 4:
    fourth quadrant
10:

The region represented by the inequalities
x ≥ 6, y ≥ 2, 2x + y ≤ 0, x ≥ 0, y ≥ 0 is


Correct
  • 1:
    unbounded
  • 2:
    a polygon
  • 3:
    exterior of a triangle
  • 4:
    None of these
11:

The minimum value of Z = 4x + 3y subjected to the constraints 3x + 2y ≥ 160, 5 + 2y ≥ 200, 2y ≥ 80; x, y ≥ 0 is


Correct
  • 1:
    220
  • 2:
    300
  • 3:
    230
  • 4:
    none of these
12:

The maximum value of Z = 3x + 2y, subjected to x + 2y ≤ 2, x + 2y ≥ 8; x, y ≥ 0 is


Correct
  • 1:
    32
  • 2:
    24
  • 3:
    40
  • 4:
    none of these
13:

Maximize Z = 11x + 8y, subject to x ≤ 4, y ≤ 6, x ≥ 0, y ≥ 0.


Correct
  • 1:
    44 at (4, 2)
  • 2:
    60 at (4, 2)
  • 3:
    62 at (4, 0)
  • 4:
    48 at (4, 2)
14:

Maximize Z = 10×1 + 25×2, subject to 0 ≤ x1 ≤ 3, 0 ≤ x2 ≤ 3, x1 + x2 ≤ 5.


Correct
  • 1:
    80 at (3, 2)
  • 2:
    75 at (0, 3)
  • 3:
    30 at (3, 0)
  • 4:
    95 at (2, 3)
15:

Maximize Z = 6x + 4y, subject to x ≤ 2, x + y ≤ 3, -2x + y ≤ 1, x ≥ 0, y ≥ 0.


Correct
  • 1:
    12 at (2, 0)
  • 2:
    140/3 at (2/3, 1/3)
  • 3:
    16 at (2, 1)
  • 4:
    4 at (0, 1)
16:

Maximize Z = 3x + 5y, subject to x + 4y ≤ 24, 3x + y ≤ 21, x + y ≤ 9, x ≥ 0, y ≥ 0.


Correct
  • 1:
    20 at (1, 0)
  • 2:
    30 at (0, 6)
  • 3:
    37 at (4, 5)
  • 4:
    33 at (6, 3)

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A level Linear Programming Quiz 1
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