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Quiz Chapter 7: Linear Programming

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

Question 1 of 10Score: 0

Which inequality correctly represents the statement 'The number of item Y is at least twice the number of item X'?

Full Question List & Answer Key

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

1. Which inequality correctly represents the statement 'The number of item Y is at least twice the number of item X'?

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

'At least' corresponds to the greater-than-or-equal-to symbol (≥). Thus, y ≥ 2x.

2. 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.

3. 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).

4. If the total number of items x and y must be at least 40, which inequality is correct?

  1. x + y ≥ 40
  2. x + y ≤ 40
  3. x + y > 40
  4. x - y ≥ 40
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Answer: A

'At least 40' translates to greater than or equal to 40, so x + y ≥ 40.

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. 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.

7. If an objective function parallel line is drawn as 2x + y = k, what is the gradient of this search line?

  1. -2
  2. 2
  3. -12
  4. 12
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Answer: A

Rearranging 2x + y = k into slope-intercept form gives y = -2x + k. The gradient m = -2.

8. 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.

9. 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.

10. 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.

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