MRSM Trial 2025 Add Maths Paper 2, Question 13Linear Programming

Roy's Collection is a clothing boutique that accepts orders for trousers and shirts. Table 2 shows the preparation and sewing time per item — Trousers: preparation 45 min, sewing 50 min; Shirt: preparation 30 min, sewing 70 min. The maximum preparation time is A hours and the sewing time is at least 5 hours 50 minutes. In a certain period the boutique prepares x trousers and y shirts, and the ratio of trousers to shirts successfully prepared does not exceed 4 : 5.

(a) The inequality involving the maximum preparation time A hours is represented by the straight line given on the graph paper. Find the value of A.

Roy's Collection (trousers: prep 45 min, sewing 50 min; shirt: prep 30 min, sewing 70 min; max preparation A = 10 hours; sewing at least 5 h 50 min; ratio trousers : shirts does not exceed 4 : 5; x trousers, y shirts).

(b) Write two inequalities other than the inequality in (a), x ≥ 0 and y ≥ 0, that satisfy all of the above constraints.

Roy's Collection, with constraints 45x + 30y ≤ 600, 50x + 70y ≥ 350, x/y ≤ 4/5, x ≥ 0, y ≥ 0.

(c) Construct and label the region R which satisfies all constraints.

Roy's Collection, region R as constructed. The price of a pair of trousers and a shirt is RM350 and RM200 respectively.

(d) It is given that the boutique successfully prepared x pairs of trousers and y shirts within 2 days. By using the objective function, determine whether the boutique is able to continue its operation if the monthly cost is RM40 000.