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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. 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.

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. 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.

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. 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. 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.

8. Which phrase indicates the inequality symbol '≤'?

  1. At most
  2. At least
  3. More than
  4. Not less than
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Answer: A

'At most' means maximum limit, which is represented by the less-than-or-equal-to symbol (≤).

9. 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.

10. A bakery makes x chocolate cakes and y cheese cakes. 'The number of cheese cakes is not more than 3 times the number of chocolate cakes.' Which inequality represents this?

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

Cheese cakes (y) 'is not more than' (≤) 3 times chocolate cakes (x), so y ≤ 3x.

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