SPM 2022 Add Maths Paper 2, Question 13Linear Programming

A factory produces guava juice and watermelon juice. Due to a limitation on production capacity, the factory can produce at most 180 packs of juice in a day. The number of packs of watermelon juice produced exceeds the number of packs of guava juice by less than 60 packs. The demand for the number of packs of watermelon juice is at least 1/2 of the number of packs of guava juice.

(a) In a day, the factory produces x packs of guava juice and y packs of watermelon juice. Write three inequalities other than x ≥ 0 and y ≥ 0 that satisfy all the above constraints.

(b) Using a scale of 2 cm to 20 packs on both axes, construct and shade the region R which satisfies all the above constraints (x + y ≤ 180, y − x < 60, y ≥ (1/2)x, x ≥ 0, y ≥ 0).

Use the graph constructed in 13(b) to answer the following:

(c) (i) State the maximum number of packs of guava juice produced. (ii) Due to an increase in the price of guava on a particular day, each pack of guava juice causes a loss of RM5.50. The profit from each pack of watermelon juice is RM40. If the factory has produced 80 packs of watermelon juice on that day, calculate the maximum profit obtained.