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ECZ Grade 12 School Certificate Linear Programming — practice questions

Explore 29 free Linear Programming questions in ECZ Grade 12 School Certificate Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Linear Programming questions and exercises with answers

Showing questions 1–29 of 29.

In an optimisation problem, what are the limitations of the situation called?Read the answer and worked solution →A profit is described by P equals 5x plus 8y. What is the profit when x is 4 and y is 6?Read the answer and worked solution →A constraint states that x plus 2y must not be more than 20. Is the pair x equal to 6 and y equal to 8 allowed?Read the answer and worked solution →Complete the definition of conditional probabilityRead the answer and worked solution →True or false: conditional probabilityRead the answer and worked solution →Independent or mutually exclusive?Read the answer and worked solution →Match each rule to its nameRead the answer and worked solution →IndependenceRead the answer and worked solution →Order the steps for a Bayes' theorem questionRead the answer and worked solution →Complete the conditions for a partitionRead the answer and worked solution →True or false: independence versus exclusivityRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →Tap every statement that follows from independenceRead the answer and worked solution →The multiplication ruleRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Complete the theorem of total probabilityRead the answer and worked solution →Which theorem answers which question?Read the answer and worked solution →True or false: total probability and BayesRead the answer and worked solution →Match each historical figure to their contributionRead the answer and worked solution →The Historical NoteRead the answer and worked solution →Flip and pair: notation with meaningRead the answer and worked solution →Order the reasoning: from a partition to a posteriorRead the answer and worked solution →Tap every quantity that is a probabilityRead the answer and worked solution →Spot the odd one outRead the answer and worked solution →Assertion and reason: the multiplication ruleRead the answer and worked solution →True or false: the Historical NoteRead the answer and worked solution →Sort each statement by which idea it describesRead the answer and worked solution →

Worked practice questions

In an optimisation problem, what are the limitations of the situation called?

  1. Constraints
  2. Objectives
  3. Variables
  4. Solutions
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Correct answer: A. Constraints

1. Every optimisation problem carries limits on what can be done. 2. Those limitations are called constraints. 3. Each constraint is written down as an inequality before any graph is drawn. _Source: Siyavula Mathematics Grade 11 (Everything Maths, CC BY 4.0), Chapter 12: Linear programming_

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A profit is described by P equals 5x plus 8y. What is the profit when x is 4 and y is 6?

  1. It is 68
  2. It is 58
  3. It is 78
  4. It is 48
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Correct answer: A. It is 68

1. The equation that is to be made as large as possible is the objective function. 2. Substitute the given values into it one term at a time. 3. Five times 4 is 20. 4. Eight times 6 is 48. 5. Adding the two terms gives 20 plus 48, which is 68. 6. Answering 48 uses only the second term and drops the first one. _Source: Siyavula Mathematics Grade 11 (Everything Maths, CC BY 4.0), Chapter 12: Linear programming_

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A constraint states that x plus 2y must not be more than 20. Is the pair x equal to 6 and y equal to 8 allowed?

  1. Yes, it gives 20
  2. No, it gives 22
  3. Yes, it gives 14
  4. No, it gives 28
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Correct answer: B. No, it gives 22

1. A constraint is written as an inequality that any acceptable pair of values must satisfy. 2. Substitute the given values into the left hand side of the inequality. 3. x is 6, so the first term is 6. 4. y is 8, so 2y is 2 times 8, which is 16. 5. Adding the terms gives 6 plus 16, which is 22. 6. The constraint allows no more than 20, and 22 is greater than 20. 7. So the pair lies outside the feasible region and is not allowed. 8. Answering 14 subtracts the two terms instead of adding them. _Source: Siyavula Mathematics Grade 11 (Everything Maths, CC BY 4.0), Chapter 12: Linear programming_

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