SPM 2017 Add Maths Paper 2, Question 14Linear Programming

Use a graph paper to answer this question. An entrepreneur wants to produce two types of toys, P and Q by using a machine. In a day, the machine produces x number of type P toys and y number of type Q toys. The time required to produce a type P toy is 6 minutes and the time required to produce a type Q toy is 5 minutes. The production of the toys is based on the following constraints: I: The total number of toys produced must be more than 40 units in a day. II: The machine can operate for only 15 hours a day. III: The ratio of the number of type P toys to the number of type Q toys is at most 3:5. (a) 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 toys on both axes, construct and shade the region R which satisfies all the above constraints. (c) Using the graph constructed in 14(b), find the range of total sales that can be obtained if the selling price of a type P toy is RM5 and the selling price of a type Q toy is RM3.