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

Solved on video in English · Form 5, Linear Programming · 6:15 video

The question

(a)

Table 3 gives, per cake, the mass (kg) of flour, sugar and margarine, the cost and the selling price for two cakes. Chocolate cake: flour 0.4, sugar 0.1, margarine 0.1, cost RM35, selling price RM70. Vanilla cake: flour 0.1, sugar 0.2, margarine 0.1, cost RM30, selling price RM50. To minimise cost, at least 8 kg of flour and at least 6 kg of sugar are used, and the maximum mass of margarine used is 5 kg. The shop produces x chocolate cakes and y vanilla cakes. (a) Write three inequalities, other than x ≥ 0 and y ≥ 0, that satisfy all the constraints above.

(b)

(b) Using a scale of 2 cm to 10 chocolate cakes on the x-axis and 2 cm to 5 vanilla cakes on the y-axis, construct and shade the region R which satisfies all the above constraints.

(c)(i)

(c) Use the graph constructed in 15(b) to answer the following: (i) Calculate the maximum profit obtained.

(c)(ii)

(c)(ii) Hence, find the mass of flour that needs to be used.

Selangor Trial 2025 Add Maths Paper 2, Question 15: the question as drawn in Eduly's video6:15

Part (a)

Step 1

Flour: chocolate uses 0.4 kg and vanilla 0.1 kg per cake, and at least 8 kg is used: 0.4x + 0.1y ≥ 8.

Why this step

'At least' means 8 kg is the minimum, so we use ≥. Also match 0.4 to chocolate (x) and 0.1 to vanilla (y), not the other way round.

3 more steps, each with the reason for it, in the full solution

Final answer

0.4x + 0.1y ≥ 8; 0.1x + 0.2y ≥ 6; 0.1x + 0.1y ≤ 5

Where students lose marks

Watch out: 'at least' means ≥ and 'maximum' means ≤. Also keep chocolate (x) and vanilla (y) coefficients in the right order.

Part (b)

4 more steps, each with the reason for it, in the full solution

Final answer

Region R shaded and labelled (see video)

Where students lose marks

Watch out: check each intercept, shade the correct side of every line (≥ away from the origin, ≤ towards it), and label R.

Part (c)(i)

3 more steps, each with the reason for it, in the full solution

Final answer

Maximum profit = RM1600 at (40, 10)

Where students lose marks

Watch out: maximise profit 35x + 20y (selling price minus cost), not selling price 70x + 50y, and check the corner (40, 10).

Part (c)(ii)

2 more steps, each with the reason for it, in the full solution

Final answer

17 kg

Where students lose marks

Watch out: use the profit-maximising point (40, 10) and the flour expression 0.4x + 0.1y, not the sugar or margarine one.

Watch every step of this question solved on video (6:15), with the reason behind each step and a box that checks your own answer.

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