Melaka Trial 2025 Add Maths Paper 2, Question 15Linear Programming

Use graph paper to answer this question. A private higher education institution A offers two courses, Engineering and Medicine. The number of students for Engineering is x and for Medicine is y. The intake is based on the following constraints: I. The minimum number of Engineering students is 200 and the maximum is 500. II. The total number of students in both courses does not exceed 700. III. The number of Engineering students exceeds twice the number of Medicine students by at most 200.

(a) Write three inequalities, other than x ≥ 0 and y ≥ 0, that satisfy all the above constraints.

Using the inequalities 200 ≤ x ≤ 500, x + y ≤ 700 and x − 2y ≤ 200:

(b) Using a scale of 2 cm to 100 students on both axes, construct and shade the region R which satisfies all the above constraints.

Using the graph constructed in 15(b):

(c)(i) Find the maximum number of Medicine students that can be taken if the number of Engineering students is 250.

Using the graph constructed in 15(b):

(c)(ii) Find the maximum amount of fees that can be collected per semester if the fee for each Engineering student for one semester is RM600 and for a Medicine student is RM800.