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SMK Teknologi dan Rekayasa

Soal 37 Nilai Optimum (Program Linear)


Nilai\ minimum\ dari\ \ z=2x+3y\ \ pada\ daerah\ yang\ diarsir\\dari\ gambar\ di\ bawah\ adalah\ ....

a.\ \ 20\ \ \ \ \ \ \ \ \ \ b.\ \ 21\ \ \ \ \ \ \ \ \ \ c.\ \ 22\ \ \ \ \ \ \ \ \ \ d.\ \ 23\ \ \ \ \ \ \ \ \ \ e.\ \ 24
Jawaban: e

Persamaan\ garis:
(1)\ \ yang\ melalui\ titik\ (0,\ 12)\ dan\ (6,\ 0)\ \ \to \ \ b=12,\ a=6
\begin{array}{rcl}bx+ay&=&b.a\\12x+6y&=&12.6\\2x+y&=&12\end{array}
(2)\ \ yang\ melalui\ titik\ (0,\ 8)\ dan\ (12,\ 0)\ \ \to \ \ b=8,\ a=12
\begin{array}{rcl}bx+ay&=&b.a\\8x+12y&=&8.12\\2x+3y&=&24\end{array}
Perpotongan\ kedua\ garis:
\frac{\begin{matrix} 2x+y=12\\ 2x+3y=24 \end{matrix}}{}\ -\\\ \ \ \ \ \ \ -2y=-12\\y=6
2x+y=12\\2x+6=12\\2x=6\\x=3
Koordinat\ titik\ potong\ kedua\ garis\ adalah\ (3,\ 6)
\mathbf{Penentuan\ nilai\ optimum}:

Jadi\ nilai\ minimum\ dari\ \ z=2x+3y\ \ adalah\ 24.

About Kalakay

Guru Matematika SMK

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One thought on “Soal 37 Nilai Optimum (Program Linear)

  1. Sepertinya kebalik. yang y jd x, yg x jd y.

    Posted by Alil Markolil | 19 September 2012, 8:06 PM

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