Kuala Lumpur Trial 2025 Add Maths Paper 2, Question 12Linear Programming

Puan Anisah produces two types of products, chocolate cakes and potato bread. Each product requires two ingredients, wheat flour and sugar. The ingredients needed to make one chocolate cake and one potato bread are shown in Table 2: a chocolate cake needs 300 g wheat flour and 100 g sugar; a potato bread needs 150 g wheat flour and 200 g sugar. She has 12 kg of wheat flour and 7 kg of sugar. The number of chocolate cakes produced is more than two-thirds the number of potato breads. She produces x chocolate cakes and y potato breads.

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

Puan Anisah produces x chocolate cakes and y potato breads subject to the constraints in part (a).

(b) Using a scale of 2 cm to 10 units on both axes, construct and shade the region R which satisfies all the above constraints.

Puan Anisah produces x chocolate cakes and y potato breads subject to the constraints in part (a), with region R drawn in part (b).

(c) Based on the graph obtained in (b), find: (i) the maximum number of potato bread that can be produced if the shop produces 20 chocolate cakes.

(c)(ii) the maximum profit obtained by Puan Anisah if the profit from selling a chocolate cake and a potato bread are RM20 and RM25 respectively.