SPM 2021 Add Maths Paper 2, Question 15Linear Programming

The Additional Mathematics Panel will organise a Seminar Skor for some students from class A and class B. The number of students from class A is x and the number of students from class B is y. The selection is based on the following constraints: I. The maximum number of students is 80. II. The number of students from class B that exceeds the number of students from class A is less than 10. III. The minimum number of students from class B is 15. (a) Write three inequalities, other than x ≥ 0 and y ≥ 0, which satisfy all the above constraints.

Given the constraints x + y ≤ 80, y − x < 10, y ≥ 15 (with x ≥ 0, y ≥ 0): (b) Using a scale of 2 cm to 10 students on both axes, construct and shade the region R which satisfies all the above constraints.

Use the graph constructed in part (b) to answer: (c)(i) Find the maximum number of students from class B. (c)(ii) All students who participate in the seminar have to pay a registration fee. Every student from class B has paid a deposit of RM4, while students from class A make the full payment on that day. Calculate the balance of payment that has to be paid by each student from class B such that the number of students from class B is maximum and the total collection from all students on that day is RM400.