Contoh Soal 2 Program Linear (Matematika Wajib Kelas XI)

 $\begin{array}{l}\\ 6.& \text{Pada gambar berikut ini, yang merupakan}\\ & \text{himpunan penyelesaian sistem pertidaksamaan}\\ \\ & \{\begin{array}{ll}-x+2y& \le 2\\ 4x+3y& \le 12\\ x\ge 0& \\ y\ge 0& \end{array}\\ \\ & \text{adalah}....\end{array}$

$.\begin{array}{l}\\ & \begin{array}{l}\\ \text{a}.& \text{I}\\ \text{b}.& \text{II}\\ \text{c}.& \text{III}\\ \text{d}.& \text{I}\text{dan}\text{IV}\\ \text{e}.& \text{II}\text{dan}\text{II}\end{array}\\ \\ & \text{Jawab}:\mathbf{\text{a}}\\ & \text{Pembahasan diserahkan kepada pembaca}\end{array}$

$\begin{array}{l}\\ 7.& \text{Pada gambar berikut ini, yang merupakan}\\ & \text{himpunan penyelesaian sistem pertidaksamaan}\\ \\ & \{\begin{array}{ll}5x+y& \ge 10\\ 2x+y& \le 8\\ y\ge 2& \end{array}\\ \\ & \text{adalah}....\end{array}$

$.\begin{array}{l}\\ & \begin{array}{l}\\ \text{a}.& \text{I}\\ \text{b}.& \text{II}\\ \text{c}.& \text{III}\\ \text{d}.& \text{IV}\\ \text{e}.& \text{V}\end{array}\\ \\ & \text{Jawab}:\mathbf{\text{c}}\\ & \text{Pembahasan diserahkan kepada pembaca}\end{array}$

$\begin{array}{l}\\ 8.& \text{Pada gambar berikut ini, yang merupakan}\\ & \text{himpunan penyelesaian sistem pertidaksamaan}\\ \\ & \{\begin{array}{ll}x+y& \ge 4\\ x+2y& \le 6\\ y\ge 1& \end{array}\\ \\ & \text{adalah}....\end{array}$

$.\begin{array}{l}\\ & \begin{array}{l}\\ \text{a}.& \text{I}\\ \text{b}.& \text{II}\\ \text{c}.& \text{III}\\ \text{d}.& \text{IV}\\ \text{e}.& \text{V}\end{array}\\ \\ & \text{Jawab}:\mathbf{\text{c}}\\ & \text{Pembahasan juga diserahkan kepada pembaca}\end{array}$

$\begin{array}{l}\\ 9.& (\text{SPMB 2003})\\ & \text{Daerah yang diarsir pada ilustrasi gambar berikut}\\ & \text{adalah himpunan semua}(x,y)\text{yang memenuhi}\end{array}$

$.\begin{array}{l}\\ \text{a}.& 2x+y\le 30,3x+4y\le 60,x\ge 0,y\ge 0\\ \text{b}.& 2x+y\ge 30,3x+4y\ge 60,x\ge 0,y\ge 0\\ \text{c}.& x+2y\ge 30,3x+4y\ge 60,x\ge 0,y\ge 0\\ \text{d}.& x+2y\le 30,4x+3y\le 60,x\ge 0,y\ge 0\\ \text{e}.& 2x+y\ge 30,4x+3y\le 60,x\ge 0,y\ge 0\end{array}$

$.\begin{array}{rl}& \text{Jawab}:\mathbf{\text{a}}\\ & \text{Persamaan garisnya adalah}:\\ & (1)15x+20y=300\\ & \text{kendala}:3x+4y\le 60\\ & (2)30x+15y=450\\ & \text{kendala}:2x+y\le 30\\ & (3)y=0,\text{kendala}:y\ge 0\\ & (4)x=0,\text{kendala}:x\ge 0\end{array}$

$\begin{array}{l}\\ 10.& (\text{SPMB 2004})\\ & \text{Daerah yang diarsir pada ilustrasi gambar berikut}\\ & \text{adalah himpunan penyelesaian yang dipenuhi oleh}\end{array}$

$.\begin{array}{l}\\ \text{a}.& 6x+5y-30\le 0,x+6y-6\le 0,x-y\le 0\\ \text{b}.& 6x+5y-30\ge 0,x+6y-6\le 0,x-y\le 0\\ \text{c}.& 6+5y-30\le 0,x+6y-6\ge 0,x-y\ge 0\\ \text{d}.& 6x+5y-30\le 0,x+6y-6\ge 0,x-y\le 0\\ \text{e}.& 6x+5y-30\ge 0,x+6y-6\ge 0,x-y\ge 0\end{array}$

$.\begin{array}{rl}& \text{Jawab}:\mathbf{\text{c}}\\ & \text{Perhatikan bahwa kendala-kendalanya}:\\ & \begin{array}{|ccc|}\hline \begin{array}{rl}6x+5y& =6\times 5\\ 6x+5y& =30\end{array}& \begin{array}{rl}x+6y& =1\times 6\\ x+6y& =6\end{array}& \begin{array}{rl}x& =y\end{array}\\ \mathbf{\text{Sebelah kiri}}& \mathbf{\text{Sebelah kanan}}& \\ \begin{array}{rl}6x+5y& \le 30\\ 6x+5y-30& \le 0\end{array}& \begin{array}{rl}x+6y& \ge 6\\ x+6y-6& \ge 0\end{array}& \begin{array}{rl}x& \ge y\\ x-y& \ge 0\end{array}\\ \hline\end{array}\end{array}$