
Alloy mixture optimization (Minimize Expenses)There are four metals A, B, C and D that have the following properties:
Metal  Density (den)  Carbon (crb), %  Phosphor (psh), %  Price, $ / kg 
A  6500  0.2  0.05  2.0 
B  5800  0.35  0.015  2.5 
C  6200  0.15  0.065  1.5 
D  5900  0.11  0.1  2.0 
The is a requirement to produce an alloy at minimal cost that has the following property ranges:
Range  Density (den)  Carbon (crb), %  Phosphor (psh), % 
Min  5950  0.1  0.045 
Max  6050  0.3  0.055 
The decision variables are part of each metals in the alloy: X_A,
X_B, X_C and X_D.
The objective function that to be minimized is:
F = X_A * A_Price + X_B * B_Price + X_C * C_Price + X_D * D_Price.
The density constraints are:
X_A * A_den + X_B * B_den + X_C * C_den + X_D * D_den >= 5950
X_A * A_den + X_B * B_den + X_C * C_den + X_D * D_den <= 6050
The carbon concentration constraints are:
X_A * A_crn + X_B * B_crn + X_C * C_crn + X_D * D_crn >= 0.1
X_A * A_crn + X_B * B_crn + X_C * C_crn + X_D * D_crn <= 0.3
The phosphor concentration constraints are:
X_A * A_psh + X_B * B_psh + X_C * C_psh + X_D * D_psh >= 0.045
X_A * A_psh + X_B * B_psh + X_C * C_psh + X_D * D_psh <= 0.055
We have to define the part of each metals in the alloy, therefore the last constraints
is:
X_A + X_B + X_C + X_D = 1
The problem has been solved successfully with the following plan:
Metal  Metal Part 
A   
B  0.285 
C  0.595 
D  0.12 
The Total cost of the alloy is $1.84
Linear programming examples
There are several examples of linear programming intended to make the users of GIPALS familiar with it. These examples are included in GIPALS installation and can be found in ..\GIPALS\Examples folder.
 Transport problem
 Production (profit maximization) problem
 Dietary optimization
 Alloy mixture optimization
See Screen Shots: Variables Page  Calculation Process  Constraint Page (Compact view)  Matrix Palette Dialog  Result Page  Debug Options Dialog
GIPALS Linear Programming $197.95  15000 Constraints & Variables  $297.00  Unlimited Number of Constraints & Variables
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