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selesaikan model tersebut dengan menggunakan matriks songsangan secara berangka tepat kepada 2 tempat perpuluhan

INSTRUCTIONS TO CANDIDATES
ANSWER ALL QUESTIONS

1. Sebuah bot bergerak sejauh 60km ke hilir selama 4 jam dan kemudian mengambil masa 5 jam bergerak ke hulu untuk kembali ke jeti. A boat travelled 60km downstream for 4 hours and then took 5 hours travelling upstream to return to the jetty.

(a) Rumuskan suatu sistem persamaan linear untuk mengira kelajuan bot dalam air pegun dan kelajuan arus sungai. Formulate a system of linear equations to calculate the speed of the boat in still water and the speed of the river current. (2 markah/marks)

(b) Selesaikan model tersebut dengan menggunakan matriks songsangan secara berangka tepat kepada 2 tempat perpuluhan. Solve the model using the matrix inverse numerically precise to 2 decimal places. (2 markah/marks)

2. Seorang ahli politik tempatan sedang membuat anggaran belanjawan untuk kempen medianya. Dia akan mengagihkan dana antara iklan TV dan iklan radio. Dia telah diberi nasihat berikut oleh penasihat kempennya. Dia harus menyiarkan sekurang-kurangnya 130 iklan TV dan sekurang-kurangnya 35 iklan radio. Bilangan iklan TV yang disiarkannya mestilah sekurangkurangnya dua kali bilangan iklan radio yang disiarkannya tetapi tidak lebih dari tiga kali bilangan iklan radio yang disiarkannya. Kos iklan TV adalah RM9,500 per iklan dan kos iklan radio adalah RM3,000 per iklan. A local politician is budgeting for her media campaign. She will distribute her fund between TV ads and radio ads. She has been given the following advice by her campaign advisers. She should run at least 130 TV ads and at least 35 radio ads. The number of TV ads she runs should be at least twice the number of radio ads she runs but not more than three times the number of radio ads she runs. The cost of a TV ad is RM9,500 and the cost of a radio ad is RM3,000.

(a) Rumuskan fungsi objektif dan kekangan untuk pengaturcaraan linear ini. Formulate the objective function and constraints for this linear programming. (4 markah/marks)

(b) Selesaikan pengaturcaraan linear ini dengan menggunakan Microsoft Excel. Gabungan iklan TV dan radio yang manakah harus dipilih untuk meminimumkan kos kempen medianya? Solve this linear programming using Microsoft Excel. Which combination of TV and radio ads should she choose to minimize the cost of her media campaign? (4 markah/marks)

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