Question 15:
Additional Mathematics Panel will organise Seminar Skor for some of the 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 number of students selected 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. [3 marks]
(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. [3 marks]
(c) Use the graph constructed in 15(b) to answer the following questions:
(i) Find the maximum number of students from class B.
(ii) All students that participate in the seminar have to pay a registration fee. Every student from class B has paid a deposit of RM4 while the students from class A will 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.
[4 marks]
Answer:
(a)
I : x + y ≤ 80
II : y – x < 10
III : y ≥ 15
(b)
(c)(i) 44
(c)(ii) $$ \begin{aligned} & \text { Maximum point }=(36,44) \\ & a(36)+4(36)+a(44)=400 \\ & 80 a=400-144 \\ & a=3.2 \end{aligned} $$
$$ \begin{aligned} &\text { The balance of payment by a student of class } B\\ &\text { = RM3.20 } \end{aligned} $$
Additional Mathematics Panel will organise Seminar Skor for some of the 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 number of students selected 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. [3 marks]
(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. [3 marks]
(c) Use the graph constructed in 15(b) to answer the following questions:
(i) Find the maximum number of students from class B.
(ii) All students that participate in the seminar have to pay a registration fee. Every student from class B has paid a deposit of RM4 while the students from class A will 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.
[4 marks]
Answer:
(a)
I : x + y ≤ 80
II : y – x < 10
III : y ≥ 15
(b)
(c)(i) 44
(c)(ii) $$ \begin{aligned} & \text { Maximum point }=(36,44) \\ & a(36)+4(36)+a(44)=400 \\ & 80 a=400-144 \\ & a=3.2 \end{aligned} $$
$$ \begin{aligned} &\text { The balance of payment by a student of class } B\\ &\text { = RM3.20 } \end{aligned} $$