SPM 2018 Add Maths Paper 2, Question 15Linear Programming

Use the graph paper provided on page 23 to answer this question. Detach the graph paper and tie it together with your answer booklet. A department store sells two types of perfumes, P and Q. The selling price of perfume P is RM400 per bottle and perfume Q is RM100 per bottle. A promoter, Zie sells x bottles of perfume P and y bottles of perfume Q. She will be given a 5% commission of her total sales if she is able to achieve the following targets: I. The total number of bottles of perfume sold is at least 50. II. The minimum total sale is RM8 000. (a) Write two inequalities, other than x >= 0 and y >= 0, which satisfy all the above constraints. (b) Use a scale of 2 cm to 10 bottles on both axes, construct and shade the region R which satisfies all the above constraints. (c) Use the graph constructed in 15(b) to answer the following questions: (i) Find the minimum number of bottles of perfume P and perfume Q to be sold if the number of bottles of perfume Q sold is twice the number of bottles of perfume P. (ii) Determine the minimum amount of commission received by Zie if she is able to sell 35 bottles of perfume P.