SPM 2019 Add Maths Paper 2, Question 14Linear Programming

Use the graph paper provided to answer this question. Siti is assigned to prepare prizes in conjunction with STEM Week. She is required to purchase x set of pens and y set of notebooks. The price for a set of pens is RM3 and the price for a set of notebooks is RM4. The purchase of the prizes is based on the following constraints: I. The total number of set of pens and set of notebooks must be more than 40. II. The total allocation is RM400. III. The number of set of pens exceed the number of set of notebooks by at most 10. (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 10 sets on both axes, construct and shade the region R which satisfies all the above constraints. (c) Use the graph constructed in 14(b) to answer: (i) Find the minimum balance of the allocation, if the number of set of pens purchased is equal to the number of set of notebooks. (ii) Determine the maximum number of set of pens that can be purchased if Siti spent RM50 for wrapping papers.