Question 1

If a manufacturing process is defined by two constraints (time and material), what name is given to the process by which output can be maximised?

Accepted Answer

A)  Linear programming 
B)  Optimisation 
C)  Inequality matching 
D)  Throughout constraining 
A)  Linear programming 
B)  Optimisation 
C)  Inequality matching 
D)  Throughout constraining A

Question 2

In a linear programming problem how can the optimum, maximising, solution be identified?

Accepted Answer

A)  The point within the feasibility region, intersecting the line defining the objective function, furthest up the vertical (y) axis 
B)  The point within the feasibility region, intersecting the line defining the objective function, furthest along the horizontal (x) axis 
C)  The point within the feasibility region, intersecting the line defining the objective function, that is closest to the origin 
D)  The point within the feasibility region, intersecting the line defining the objective function, that is furthest away from the origin 
A)  The point within the feasibility region, intersecting the line defining the objective function, furthest up the vertical (y) axis 
B)  The point within the feasibility region, intersecting the line defining the objective function, furthest along the horizontal (x) axis 
C)  The point within the feasibility region, intersecting the line defining the objective function, that is closest to the origin 
D)  The point within the feasibility region, intersecting the line defining the objective function, that is furthest away from the origin D

Question 3

Which of the following statements about linear inequalities is NOT true?

Accepted Answer

A)  Linear inequalities define areas rather than lines 
B)  The inequality x<6 defines an area above the line y = x 
C)  Equalities define straight lines 
D)  The inequality 2y + 3x < 8 defines an area below and to the left of the line 2y + 3x = 8 
A)  Linear inequalities define areas rather than lines 
B)  The inequality x<6 defines an area above the line y = x 
C)  Equalities define straight lines 
D)  The inequality 2y + 3x < 8 defines an area below and to the left of the line 2y + 3x = 8 B

Question 4

A shipping company has two sizes of box (l & s). If the large size is 4 times the volume of the smaller, which of the following inequalities defines the feasibility region for packing a container?

Accepted Answer

A)  l + 4s ≤ 32 
B)  l - 4s ≤ 32 
C)  4l + s ≤ 32 
D)  4l - s ≤ 32 
A)  l + 4s ≤ 32 
B)  l - 4s ≤ 32 
C)  4l + s ≤ 32 
D)  4l - s ≤ 32

Question 5

A manufacturing firm can make 2 products (a & b). If the feasibility region for their work is given by the inequality 34a + 23b < 600 what is the maximum number of product a that can be made?

Accepted Answer

A)  16 
B)  17 
C)  18 
D)  19 
A)  16 
B)  17 
C)  18 
D)  19

Question 6

In a linear programming problem how can the optimum, minimising, solution be identified?

Accepted Answer

A)  The point within the feasibility region, intersecting the line defining the objective function, furthest up the vertical (y) axis 
B)  The point within the feasibility region, intersecting the line defining the objective function, furthest along the horizontal (x) axis 
C)  The point within the feasibility region, intersecting the line defining the objective function, that is closest to the origin 
D)  The point within the feasibility region, intersecting the line defining the objective function, that is furthest away from the origin 
A)  The point within the feasibility region, intersecting the line defining the objective function, furthest up the vertical (y) axis 
B)  The point within the feasibility region, intersecting the line defining the objective function, furthest along the horizontal (x) axis 
C)  The point within the feasibility region, intersecting the line defining the objective function, that is closest to the origin 
D)  The point within the feasibility region, intersecting the line defining the objective function, that is furthest away from the origin

Question 7

A painting firm in Amman, Jordan can paint x number of walls and y number of windows each week. If it takes 4 hours to paint a wall and 2 hours to paint a window, and 2 painters are employed, each working 35 hours which of the options defines the feasibility region for this work?

Accepted Answer

A)  4x + 2y ≥ 70 
B)  4x - 2y ≥70 
C)  4x + 2y ≤ 70 
D)  4x - 2y ≤ 70 
A)  4x + 2y ≥ 70 
B)  4x - 2y ≥70 
C)  4x + 2y ≤ 70 
D)  4x - 2y ≤ 70

Question 8

Which of the following statements concerning a linear programming problem is NOT true?

Accepted Answer

A)  When using the graphical method for solving a linear programming problem a maximum of 2 variables can be used 
B)  When using the graphical method for solving a linear programming problem one, but not both variables can be negative 
C)  When using the graphical method for solving a linear programming problem trial and error is an acceptable method for finding the optimal point 
D)  When using the graphical method for solving a linear programming problem an algebraic method can be used to confirm the optimal point 
A)  When using the graphical method for solving a linear programming problem a maximum of 2 variables can be used 
B)  When using the graphical method for solving a linear programming problem one, but not both variables can be negative 
C)  When using the graphical method for solving a linear programming problem trial and error is an acceptable method for finding the optimal point 
D)  When using the graphical method for solving a linear programming problem an algebraic method can be used to confirm the optimal point

Question 9

Which of the following statements is NOT true?

Accepted Answer

A)  For non-linear (more complex) inequalities an alternative to the linear programming model must be used 
B)  When presenting the graphical solution to a linear programming problem as much information as possible should be shown on the diagram 
C)  The sign technique is one method that can be used to confirm that the inequality is the correct side of the corresponding defining line 
D)  An alternative method for resolving more complex linear programming problems is the 'simplex' method 
A)  For non-linear (more complex) inequalities an alternative to the linear programming model must be used 
B)  When presenting the graphical solution to a linear programming problem as much information as possible should be shown on the diagram 
C)  The sign technique is one method that can be used to confirm that the inequality is the correct side of the corresponding defining line 
D)  An alternative method for resolving more complex linear programming problems is the 'simplex' method

Question 10

Which of the following options is NOT an example of an inequality?

Accepted Answer

A)  At least 300 units must be produced this week 
B)  A maximum of 120 person hours are available 
C)  Travel expenses should not be more than €12,000 per person per year 
D)  The cost of a new water-cutting machine is AED 2.25 million 
A)  At least 300 units must be produced this week 
B)  A maximum of 120 person hours are available 
C)  Travel expenses should not be more than €12,000 per person per year 
D)  The cost of a new water-cutting machine is AED 2.25 million

Exam 35: Linear Inequalities

If a manufacturing process is defined by two constraints (time and material), what name is given to the process by which output can be maximised?

In a linear programming problem how can the optimum, maximising, solution be identified?

Which of the following statements about linear inequalities is NOT true?

A shipping company has two sizes of box (l & s). If the large size is 4 times the volume of the smaller, which of the following inequalities defines the feasibility region for packing a container?

A manufacturing firm can make 2 products (a & b). If the feasibility region for their work is given by the inequality 34a + 23b < 600 what is the maximum number of product a that can be made?

In a linear programming problem how can the optimum, minimising, solution be identified?

A painting firm in Amman, Jordan can paint x number of walls and y number of windows each week. If it takes 4 hours to paint a wall and 2 hours to paint a window, and 2 painters are employed, each working 35 hours which of the options defines the feasibility region for this work?

Which of the following statements concerning a linear programming problem is NOT true?

Which of the following statements is NOT true?

Which of the following options is NOT an example of an inequality?

Introduction to Business Mathematics and Statistics

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