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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. 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.

2. 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).

3. Translate into an inequality: 'The total capacity of cars (x) and buses (y) cannot exceed 500 passengers.'

  1. x + y ≤ 500
  2. x + y ≥ 500
  3. x + y < 500
  4. x + y = 500
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Answer: A

'Cannot exceed' means the total must be less than or equal to 500, so x + y ≤ 500.

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. 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.

6. 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.

7. 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.

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. 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 (≤).

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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