Berdasarkan sola di atas, diberikan pertidaksamaan yang dapat ditentukan daerah himpunan penyelesaiannya dengan cara menentukan titik koordinatnya terlebih dahulu.
Titik koordinat persamaan
sebagai berikut:
![](https://imgix2.ruangguru.com/assets/miscellaneous/png_esyv7y_6582.PNG)
maka daerah himpunan penyelesaian pertidaksamaan
sebagai berikut:
![](https://imgix2.ruangguru.com/assets/miscellaneous/png_yh2gzi_8481.PNG)
Daerah himpunan penyelesaian pertidaksamaan
sebagai berikut:
![](https://imgix2.ruangguru.com/assets/miscellaneous/png_nrhbr1_6780.PNG)
Daerah himpunan penyelesaian pertidaksamaan
sebagai berikut:
Sehingga, apabila ketiga daerah himpunan penyelesaian tersebut digabung maka akan diperoleh himpunan penyelesaian sebagai berikut:
![](https://imgix2.ruangguru.com/assets/miscellaneous/png_hqdrpb_9835.PNG)
Titik perpotongan garis
dan
dapat ditentukan dengan metode substitusi sebagai berikut:
![table row blank cell 3 x plus 2 y equals 24 end cell row cell x equals 2 rightwards arrow end cell cell 3 open parentheses 2 close parentheses plus 2 y equals 24 end cell row blank cell 6 plus 2 y equals 24 end cell row blank cell 2 y equals 18 end cell row blank cell y equals 9 end cell end table](data:image/png;base64,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)
maka titik perpotongannya adalah
.
Titik perpotongan garis
dan
dapat ditentukan dengan metode substitusi sebagai berikut:
maka titik perpotongannya adalah
.
Substitusikan semua titik yang dilewati daerah himpunan penyelesaian ke fungsi objektif untuk meperoleh nilai maksimum ataupun minimum dari dungsi tersebut sebagai berikut:
![table row blank cell f open parentheses x comma y close parentheses equals 8 x plus y end cell row cell open parentheses 2 comma 9 close parentheses rightwards arrow end cell cell f open parentheses 2 comma 9 close parentheses equals 8 open parentheses 2 close parentheses plus 9 equals 25 end cell row cell open parentheses 6 comma 3 close parentheses rightwards arrow end cell cell f open parentheses 6 comma 3 close parentheses equals 8 open parentheses 6 close parentheses plus 3 equals 51 end cell end table](data:image/png;base64,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)
Oleh karena itu, jawaban yang benar adalah 51. Tidak ada jawaban yang tepat pada pilihan jawaban di atas.