Peperiksaan Sebenar SPM Tahun 2013 Lembaga Peperiksaan, Kementerian Pendidikan Malaysia, Putrajaya. Matematik Tambahan Kertas 1, 2 (Additional Mathematics Paper 1, 2 SPM year 2013. Board of Examination, MOE Malaysia)
Question 15. Use the graph paper to answer this question.
A tourist boat operator provide x trips to Island A and y trips to Island B per day. The service provided is based on the following constraints:
I) The total number of trips provided is not more than 16.
II) The number of trips to Island A is not more than three times the number of trips to Island B.
III) The fare per trip to Island A is RM60 and the fare per trip to Island B is RM30. The total fare collection per day is not less than RM540.
(a) Write three inequalities, which satisfy all the above constraints.
(b) Using a scale of 2 cm to 2 trips on both axis, construct and shade the region R which satisfies all of the above constraints.
(c) Using the graph constructed in 15(b), find
(i) the minimum number of trips to Island B if 8 trips to Island A are provided per day,
(ii) the maximum total profit per day if the profit per trip to Island A is RM40 and the profit per trip to Island B is RM20.
Quotes : “I wanna hang a map of the world in my house. Then I’m gonna put pins into all the locations that I’ve traveled to. But first, I’m gonna have to travel to the top two corners of the map so it won’t fall down.“