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Quiz Chapter 7: Linear Programming

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

Question 1 of 10Score: 0

What is the primary goal of linear programming?

Full Question List & Answer Key

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

1. What is the primary goal of linear programming?

  1. To find the optimal (maximum or minimum) outcome under given linear constraints
  2. To solve non-linear quadratic equations algebraically
  3. To calculate the area under a curved graph
  4. To convert trigonometric functions into linear form
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Answer: A

Linear programming aims to optimize (maximize profit/yield or minimize cost/time) a linear objective function subject to linear constraints.

2. What type of line should be drawn on a graph for the inequality 2x + 3y < 12?

  1. Dashed line
  2. Solid line
  3. Dotted horizontal line only
  4. Thick double line
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Answer: A

Strict inequalities (< or >) are drawn as dashed lines because points on the boundary line are not included in the solution set.

3. 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.

4. 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.

5. 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.

6. Find the minimum value of C = 2x + 7y given the feasible vertices are (2, 8), (5, 2), and (8, 3).

  1. 24
  2. 60
  3. 37
  4. 19
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Answer: A

Evaluate C at each vertex: C(2,8) = 2(2)+7(8)=60; C(5,2) = 2(5)+7(2)=24; C(8,3) = 2(8)+7(3)=37. The minimum is 24.

7. 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).

8. Given the objective profit function Z = 40x + 50y, if optimal vertex coordinates are x = 15 and y = 25, calculate the maximum profit.

  1. RM1850
  2. RM1600
  3. RM2000
  4. RM1250
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Answer: A

Z = 40(15) + 50(25) = 600 + 1250 = RM1850.

9. 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.

10. 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.

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