George Rodriguez
08/09/2024 · Junior High School
Diketahui memaksimumkan \( z=8 x_{1}+5 x_{2} \) yang memenuhi kendala-kendala berikut: \( 2 x_{1}+5 x_{2} \leq 600 \) \( 4 x_{1}+3 x_{2} \leq 530 \) \( 2 x_{1}+x_{2} \leq 240 \) \( x_{1}, x_{2} \geq 0 \) a.ubahlah ke dalam bentuk kanonik b.gunakan metode simpleks untuk memaksimumkan \( Z \)
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a. Untuk mengubah ke bentuk kanonik, tambahkan variabel slack \( s_1, s_2, \) dan \( s_3 \) ke kendala-kendala. Bentuk kanonik adalah:
\[
\begin{align*}
\text{Fungsi Tujuan: } z &= 8x_1 + 5x_2 \\
\text{Kendala: } \\
2x_1 + 5x_2 + s_1 &= 600 \\
4x_1 + 3x_2 + s_2 &= 530 \\
2x_1 + x_2 + s_3 &= 240 \\
x_1, x_2, s_1, s_2, s_3 &\geq 0
\end{align*}
\]
b. Gunakan metode simpleks untuk memaksimumkan \( Z \) dengan memulai dari tabel awal dan melanjutkan iterasi hingga semua nilai di baris \( z \) menjadi non-negatif.
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