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Linear Programming · CAPE Applied Mathematics Unit 2

25 past-paper questions on Linear Programming, part of Module 1: Discrete Mathematics, from every CAPE Applied Mathematics Unit 2 paper on Quelpr.

Practise Linear Programming
  1. 1(a)12 marks· CAPE Applied Mathematics Unit 2 · 2008 (second paper) · Paper 2Formulate a linear programming model to determine the number of each product that maximizes the profit.
  2. 1(b)9 marks· CAPE Applied Mathematics Unit 2 · 2008 (second paper) · Paper 2Using the answer graph sheet provided, graph the inequalities of the linear programming model and identify the feasible region.
  3. 1(c)4 marks· CAPE Applied Mathematics Unit 2 · 2008 (second paper) · Paper 2Obtain the maximum profit and state the number of each product manufactured that gives this profit.
  4. 1(a)(i)8 marks· CAPE Applied Mathematics Unit 2 · 2010 · Paper 2On the answer sheet provided, graph the feasible region for the programming problem.
  5. 1(a)(ii)4 marks· CAPE Applied Mathematics Unit 2 · 2010 · Paper 2Hence, solve the linear programming problem.
  6. 1(a)(i)a)3 marks· CAPE Applied Mathematics Unit 2 · 2015 · Paper 2By identifying the variables, formulate the profit function that needs to be solved.
  7. 1(a)(i)b)7 marks· CAPE Applied Mathematics Unit 2 · 2015 · Paper 2Formulate the inequalities to be used to solve this problem.
  8. 1(a)(ii)a)6 marks· CAPE Applied Mathematics Unit 2 · 2015 · Paper 2On the graph sheet provided, draw the graphs of the inequalities obtained in (i) b).
  9. 1(a)(ii)b)2 marks· CAPE Applied Mathematics Unit 2 · 2015 · Paper 2Identify the feasible region to solve the problem.
  10. 1(a)(iii)a)3 marks· CAPE Applied Mathematics Unit 2 · 2015 · Paper 2From your graph, determine the number of EACH type of bottle required for maximum profit.
  11. 1(a)(iii)b)2 marks· CAPE Applied Mathematics Unit 2 · 2015 · Paper 2Determine the maximum profit.
  12. 2(a)(i)9 marks· CAPE Applied Mathematics Unit 2 · 2016 · Paper 2On the provided grid, draw the system of inequalities representing the constraints.
  13. 2(a)(ii)2 marks· CAPE Applied Mathematics Unit 2 · 2016 · Paper 2Using the same grid, shade the feasible region.
  14. 2(a)(iii)3 marks· CAPE Applied Mathematics Unit 2 · 2016 · Paper 2Use your diagram to find the maximum value of P.
  15. 1(a)(i)5 marks· CAPE Applied Mathematics Unit 2 · 2017 · Paper 2Using x for the number of acres of alfalfa and y for the number of acres of corn, formulate a linear programming problem and state clearly the maximizing function.
  16. 1(a)(ii)8 marks· CAPE Applied Mathematics Unit 2 · 2017 · Paper 2On the grid provided, draw all lines defined by the constraints and shade the feasible region satisfying all constraints.
  17. 1(a)(iii)6 marks· CAPE Applied Mathematics Unit 2 · 2017 · Paper 2Determine the number of acres of alfalfa and the number of acres of corn that the farmer must plant to maximize income.
  18. 2(a)2 marks· CAPE Applied Mathematics Unit 2 · 2018 · Paper 2Identify the TWO variables required for this problem.
  19. 2(b)4 marks· CAPE Applied Mathematics Unit 2 · 2018 · Paper 2Write the FIVE inequalities of the constraints that must be satisfied by the variables.
  20. 2(c)2 marks· CAPE Applied Mathematics Unit 2 · 2018 · Paper 2Write the objective function for this problem.
  21. 2(d)8 marks· CAPE Applied Mathematics Unit 2 · 2018 · Paper 2On the grid provided on page 9, draw the graph representing the five inequalities.
  22. 2(e)1 mark· CAPE Applied Mathematics Unit 2 · 2018 · Paper 2Label the feasible region on your graph.
  23. 2(f)3 marks· CAPE Applied Mathematics Unit 2 · 2018 · Paper 2State the coordinates of the vertices of the feasible region.
  24. 2(g)3 marks· CAPE Applied Mathematics Unit 2 · 2018 · Paper 2Determine the maximum profit.
  25. 2(h)2 marks· CAPE Applied Mathematics Unit 2 · 2018 · Paper 2State the values of the variables that give the maximum profit.

Related topics in Module 1: Discrete Mathematics