Linear Programming · CSEC Mathematics

51 past-paper questions on Linear Programming, part of RELATIONS, FUNCTIONS AND GRAPHS, from every CSEC Mathematics paper on Quelpr.

1. 10(a)1 mark· CSEC Mathematics · 2003 (Specimen) · Paper 2Mrs Cave wishes to buy x stereo sets and y television sets but the total number of sets must not exceed 20. Write an inequality in x and y to represent this information.
2. 10(b)2 marks· CSEC Mathematics · 2003 (Specimen) · Paper 2Each stereo set costs 150.00 and each television set costs 300.00, and she can spend a maximum of 4,500.00 on the sets. Write an inequality in x and y$ to represent this information.
3. 10(c)2 marks· CSEC Mathematics · 2003 (Specimen) · Paper 2She must buy at least 5 of each set. Write TWO inequalities to represent this information.
4. 10(d)6 marks· CSEC Mathematics · 2003 (Specimen) · Paper 2Using a scale of 2 cm to represent 5 units on both axes, draw on your graph the FOUR inequalities from (a), (b) and (c) above. Identify, by shading, the region satisfying the FOUR inequalities.
5. 10(e)(i)1 mark· CSEC Mathematics · 2003 (Specimen) · Paper 2The profit on each stereo is 80.00 and on each television is 100.00. Write an expression in x and y for P, the profit when all the sets are sold.
6. 10(e)(ii)2 marks· CSEC Mathematics · 2003 (Specimen) · Paper 2How many of EACH set should Mrs Cave buy in order to obtain MAXIMUM profit?
7. 10(e)(iii)1 mark· CSEC Mathematics · 2003 (Specimen) · Paper 2What is the MAXIMUM profit?
8. 8(a)(iv)1 mark· CSEC Mathematics · 2021 · Paper 2The total number of mobile phones is represented by x + y. According to the graph on page 23, what is the largest possible value of x + y?
9. 8(c)5 marks· CSEC Mathematics · 2022 · Paper 2On the grid below, plot the four lines associated with the inequalities in (a) and (b). Shade and label the region that satisfies ALL four inequalities R.
10. 8(d)(i)2 marks· CSEC Mathematics · 2022 · Paper 2Determine the two combinations for the MINIMUM number of cars and minivans that can be used to carry EXACTLY 60 people on the tour.
11. 8(d)(ii)1 mark· CSEC Mathematics · 2022 · Paper 2The company charges 75 to rent a car and 90 to rent a minivan. Show that the MINIMUM rental cost for this tour is $990.
12. 8(b)(iii)1 mark· Mathematics Q8 8(b)(iii)Show that on any given day, it is NOT possible for Mr Thomas to make 50 bottles of juice and 12 cakes.
13. 9(a)(ii)2 marks· Mathematics Q9 9(a)(ii)Identify the three pairs of (x, y) values for which P has a maximum or a minimum value.
14. 9(a)(iii)3 marks· Mathematics Q9 9(a)(iii)Which pair of (x, y) values makes P a maximum? Justify your answer.
15. 9(b)(ii)3 marks· Mathematics Q9 9(b)(ii)Identify the three pairs of (x, y) values for which p has a maximum or a minimum value.
16. 9(b)(iii)1 mark· Mathematics Q9 9(b)(iii)State the coordinates of the points which represent the vertices of the region showing the solution set.
17. 9(b)(iii)4 marks· Mathematics Q9 9(b)(iii)Which pair of (x, y) values makes p a maximum? Justify your answer.
18. 9(b)(iv)3 marks· Mathematics Q9 9(b)(iv)The florist sells a bouquet of flowers to make a profit of 3 on each rose and 4 on each orchid. Determine the MAXIMUM possible profit on the sale of a bouquet.
19. 9(b)(iv)2 marks· Mathematics Q9 9(b)(iv)Determine, from your graph, the minimum values of x and y which satisfy the conditions.
20. 10(a)(i)1 mark· Mathematics Q10 10(a)(i)Write an inequality to represent this information.
21. 10(a)(ii)1 mark· Mathematics Q10 10(a)(ii)Write an inequality to represent this information.
22. 10(a)(iii)2 marks· Mathematics Q10 10(a)(iii)Write TWO inequalities to represent this information.
23. 10(b)6 marks· Mathematics Q10 10(b)Using a scale of 2 cm to represent 10 kg on each axis, draw the graph of the FOUR inequalities in (a)(i) and (a)(ii). On your graph, shade ONLY the region which satisfies all four inequalities.
24. 10(b)7 marks· Mathematics Q10 10(b)Using a scale of 1 cm to represent 5 units on each axis, draw a graph of the THREE inequalities and label the region, R, which satisfies ALL of the inequalities.
25. 10(b)(i)1 mark· Mathematics Q10 10(b)(i)Using a scale of 2 cm to represent 5 Sonix radios and 2 cm to represent 5 Zent radios, draw the horizontal axis for 0 ≤ x ≤ 30 and the vertical axis for 0 ≤ y ≤ 25.
26. 10(b)(ii)4 marks· Mathematics Q10 10(b)(ii)On these axes, draw the four boundary lines for the four inequalities written in (a) (i), (ii) and (iii) above.
27. 10(b)(ii)2 marks· Mathematics Q10 10(b)(ii)Write the coordinates of the vertices of the region that satisfies the four inequalities (including y ≥ 0).
28. 10(b)(iii)2 marks· Mathematics Q10 10(b)(iii)Use your graph to write the coordinates of the vertices of the shaded region.
29. 10(b)(iii)2 marks· Mathematics Q10 10(b)(iii)Using your graph, state the coordinates of the vertices of the shaded region.
30. 10(b)(iii)1 mark· Mathematics Q10 10(b)(iii)Shade the region on your graph that satisfies ALL four of the inequalities written in (a) (i), (ii) and (iii) above.
31. 10(b)(iii)2 marks· Mathematics Q10 10(b)(iii)State the coordinates of the vertices of the shaded region.
32. 10(b)(iii)b)3 marks· Mathematics Q10 10(b)(iii)b)Calculate the minimum profit the company can make.
33. 10(b)(iv)2 marks· Mathematics Q10 10(b)(iv)State the coordinates of the vertices of the shaded region.
34. 10(c)7 marks· Mathematics Q10 10(c)Using a scale of 2 cm to represent 10 units on both axes, draw the graphs of ALL FOUR inequalities represented in the table above.
35. 10(c)(i)4 marks· Mathematics Q10 10(c)(i)Using your graph, determine the number of kilograms of each type of nut the vendor must sell in order to make the maximum profit.
36. 10(c)(i)2 marks· Mathematics Q10 10(c)(i)Use the coordinates of the vertices given at (b) (iii) above to determine the profit for each of those combinations.
37. 10(c)(i)1 mark· Mathematics Q10 10(c)(i)Express the TOTAL profit in terms of x and y.
38. 10(c)(ii)4 marks· Mathematics Q10 10(c)(ii)Calculate the maximum profit.
39. 10(c)(ii)3 marks· Mathematics Q10 10(c)(ii)Use the coordinates of the vertices given at (b)(iii) to determine the MAXIMUM profit.
40. 10(c)(ii)2 marks· Mathematics Q10 10(c)(ii)Calculate the maximum profit Pam makes.
41. 10(c)(ii)1 mark· Mathematics Q10 10(c)(ii)Hence, state the maximum profit that may be made.
42. 10(c)(ii)3 marks· Mathematics Q10 10(c)(ii)Calculate the maximum profit.
43. 10(c)(ii)4 marks· Mathematics Q10 10(c)(ii)Determine the number of dresses and shirts that Mrs Singh should buy to make the maximum profit.
44. 10(c)(ii)2 marks· Mathematics Q10 10(c)(ii)Calculate the MAXIMUM profit.
45. 10(c)(iii)2 marks· Mathematics Q10 10(c)(iii)If Pam buys 4 pens, show on your graph the maximum number of pencils she can buy.
46. 10(c)(iii)4 marks· Mathematics Q10 10(c)(iii)Calculate the maximum profit.
47. 10(d)4 marks· Mathematics Q10 10(d)Plot the points A, B and C on your graph. Hence determine which of the three packets satisfy ALL the conditions.
48. 10(vi)1 mark· Mathematics Q10 10(vi)Using your graph write down the coordinates of the vertices of the shaded region.
49. 10(vi)1 mark· Mathematics Q10 10(vi)Write down the coordinates of the vertices of the shaded region.
50. 10(vii)2 marks· Mathematics Q10 10(vii)Calculate the maximum fees charged.
51. 10(vii)2 marks· Mathematics Q10 10(vii)Calculate the maximum profit.