The document discusses linear programming problems in Mathcad. It defines key terms used in linear programming like decision variables, coefficients, constraints, objective functions, and nonnegativity constraints. It provides an example of how to represent a linear programming problem in Mathcad to either maximize or minimize an objective function subject to various inequality constraints, defining the decision variables, coefficients, and constraints. The document ends by indicating the end of the lesson and inviting questions.

1. 1
Aplikasi Riset Operasional
Dalam MATHCAD
Arif Rahman, ST MT

2. 2
Linear Programming
Variables
Decision variables
Structural variables
Auxiliary variables
Slack variables
Artificial variables
Coefficients
Cost coefficients
Technological coefficients
Constraint parameter or Right Hand Side value
Function
Objective or criterion function
Restriction or functional constraints
Nonnegativity constraints

3. 3
Linear Programming
Minimize f(x) = c1x1 + c2x2 + … + cnxn
Subject to
a11x1 + a12x2 + … + a1nxn ≤ b1
a21x1 + a22x2 + … + a2nxn ≤ b2
am1x1 + am2x2 + … + amnxn ≤ bm
and
x1 ≥ 0; x2 ≥ 0; … ; xn ≥ 0
Maximize or Minimize
≤ or ≥ or =
≤ 0 or ≥0 or unrestricted

4. Linear Programming
Untuk permasalahan maksimasi
Maximize(f,x)
Untuk permasalahan minimasi
Minimize(f,x)
Di mana
f  Vector koefisien fungsi tujuan (cost coefficient).
x  Matrix variabel keputusan (decision variable).
4

5. Linear Programming
Maximize f(x) = 5x0 + 4x1 + 6x2
Subject to :
x0 – x1 + x2 ≤ 20
3.x0 + 2.x1 + 4.x2 ≤ 42
3.x0 + 2.x1 ≤ 30
where x0 ≥ 0; x1 ≥ 0; x2 ≥ 0
5

6. 6
Akhir Perkuliahan…Akhir Perkuliahan…
…… Ada Yang DitanyakanAda Yang Ditanyakan

7. 6
Akhir Perkuliahan…Akhir Perkuliahan…
…… Ada Yang DitanyakanAda Yang Ditanyakan