Soal

Selesaikan masalah berikut menggunakan metode subtitusi, metode simpleks menggunakan R studio!

\(Z = 8x1 + 5x2\)

\(x1 + x2 ≤ 6\)

\(9x1 + 5x2 ≤ 45\)

\(x1, x2 ≥ 0\)

Jawab menggunakan Metode Simpleks

library(boot)

# set coefficients of the objective function
f.obj = c(8, 5)

# set matrix corresponding to coefficients of constraints by rows
f.con = matrix(c(1, 1, 9, 5), nrow = 2, byrow = TRUE)

# set right hand side coefficients
f.rhs = c(6, 45)

# final value (z)
z = simplex(a=f.obj, A1 = f.con, b1 = f.rhs, maxi = TRUE)
z

## 
## Linear Programming Results
## 
## Call : simplex(a = f.obj, A1 = f.con, b1 = f.rhs, maxi = TRUE)
## 
## Maximization Problem with Objective Function Coefficients
## x1 x2 
##  8  5 
## 
## 
## Optimal solution has the following values
##   x1   x2 
## 3.75 2.25 
## The optimal value of the objective  function is 41.25.

Kesimpulan :

• Nilai x1 adalah \(3.75\)
  

• Nilai x2 adalah \(2.25\)
  

• Nilai maksimum dari fungsi diatas adalah \(41.25\)

Referensi

• https://youtu.be/owVRg6ubf4Q?si=MpN0wBsrvideE2Yi