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Quiz Chapter 7: Linear Programming

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

Question 1 of 10Score: 0

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

Full Question List & Answer Key

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1. 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.

2. 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.

3. 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.

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. 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.

6. 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).

7. 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.

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. 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. 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
Show answer

Answer: A

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

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