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9 marksLinear Programming

CAPE Applied Mathematics Unit 2 · 2016 · Paper 2 · Question 2(a)(i)

Linear programming model: Maximize P = 6x + 4y subject to 4x + 6y ≤ 48, 4x + 2y ≤ 32, 0 ≤ y ≤ 5, x ≥ 0.

On the provided grid, draw the system of inequalities representing the constraints.

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Other parts of this question

  1. 2(a)(i)Calculate the probability that all three markers are red.[2 marks]
  2. 2(a)(ii)Calculate the probability that exactly two of the markers are black.[4 marks]
  3. 2(b)(i)Find the probability that a randomly chosen customer spends more than 8 minutes completing a transaction.[4 marks]
  4. 2(b)(ii)Find the time below which 80% of customers spend completing a transaction.[4 marks]
  5. 2(c)(i)In a random sample of 10 households, calculate the probability that exactly 6 have internet access.[4 marks]
  6. 2(c)(ii)In a random sample of 80 households, calculate the expected number that have internet access.[2 marks]
  7. 2(a)(ii)Using the same grid, shade the feasible region.[2 marks]
  8. 2(a)(iii)Use your diagram to find the maximum value of P.[3 marks]
  9. 2(b)(i)Use the Hungarian algorithm to determine the optimal assignment of each driver to a town to minimize total travel time.[9 marks]
  10. 2(b)(ii)Determine the total minimum time taken by the four drivers.[2 marks]

More practice: the rest of this paper · more Linear Programming questions · all CAPE Applied Mathematics Unit 2 past papers