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Quiz Chapter 7: Linear Programming

10 questions · Form 5 Additional Mathematics Bab 7: Linear Programming

10 questions · plays in fullscreen

Full Question List & Answer Key

Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.

1. The constraints of a linear programming problem form a feasible region R. Where do the optimal (maximum or minimum) values of the objective function always occur?

  1. At one of the vertices (corner points) of the feasible region R
  2. At the exact center of the region R
  3. On the x-intercept only
  4. Outside the region R
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Answer: A

By the fundamental theorem of linear programming, the maximum or minimum value of a linear objective function occurs at a vertex (corner point) of the feasible region.

2. When solving a linear programming problem graphically, what does a solid boundary line indicate?

  1. The inequality includes 'or equal to' (≤ or ≥)
  2. The inequality is strict (< or >)
  3. The boundary line is not part of the feasible region
  4. The objective function has no maximum value
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Answer: A

Solid lines represent inclusive inequalities (≤ or ≥), indicating points on the line are included in the solution.

3. A school hires x science teachers and y math teachers. 'The number of math teachers exceeds science teachers by at least 3.' Which inequality is correct?

  1. y - x ≥ 3
  2. x - y ≥ 3
  3. y - x ≤ 3
  4. x + y ≥ 3
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Answer: A

Difference between math (y) and science (x) is at least 3, so y - x ≥ 3.

4. The region shaded to satisfy y ≥ 2x + 1 lies:

  1. On and above the line y = 2x + 1
  2. On and below the line y = 2x + 1
  3. Strictly below the line y = 2x + 1
  4. Only in Quadrant IV
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Answer: A

For y ≥ f(x), the solution region lies on and above the boundary line y = f(x).

5. If the objective function is P = 5x + 3y, what is the value of P at the vertex point (4, 10)?

  1. 50
  2. 35
  3. 40
  4. 23
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Answer: A

Substitute x = 4 and y = 10 into P = 5(4) + 3(10) = 20 + 30 = 50.

6. A factory produces x tables and y chairs. The maximum time available is 120 hours. If each table takes 3 hours and each chair takes 2 hours, what is the constraint inequality?

  1. 3x + 2y ≤ 120
  2. 2x + 3y ≤ 120
  3. 3x + 2y ≥ 120
  4. x + y ≤ 120
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Answer: A

Total time taken is 3x + 2y, which must be less than or equal to 120 hours: 3x + 2y ≤ 120.

7. In a linear programming model, why are the constraints x ≥ 0 and y ≥ 0 almost always included?

  1. Physical quantities like items or hours cannot be negative
  2. To ensure the line passes through the origin
  3. To make the objective function equal to zero
  4. To convert strict inequalities into equations
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Answer: A

Real-world decision variables (e.g., number of chairs, hours worked) are non-negative, represented mathematically as x ≥ 0 and y ≥ 0.

8. Which of the following points lies inside the feasible region defined by x ≥ 0, y ≥ 0, x + y ≤ 6, and y ≥ x?

  1. (1, 3)
  2. (4, 1)
  3. (5, 2)
  4. (2, 1)
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Answer: A

For (1, 3): 1 ≥ 0 (True), 3 ≥ 0 (True), 1 + 3 = 4 ≤ 6 (True), and 3 ≥ 1 (True). All conditions satisfied.

9. Translate: 'The ratio of x to y is not more than 3:4'.

  1. 4x ≤ 3y
  2. 3x ≤ 4y
  3. 4x ≥ 3y
  4. xy > 34
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Answer: A

xy ≤ 34. Multiplying both sides by 4y gives 4x ≤ 3y.

10. Translate into an inequality: 'The maximum total expenditure on x books and y pens is RM150.'

  1. Cost(x) + Cost(y) ≤ 150
  2. Cost(x) + Cost(y) ≥ 150
  3. x + y > 150
  4. Cost(x) - Cost(y) ≤ 150
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Answer: A

'Maximum total' means the total sum cannot exceed RM150, represented by ≤ 150.

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