
A company can produce four different types of devices identified as A, B, C and D. The minimum amounts of devices are Amin, Bmin, Cmin and Dmin. The maximum amounts are defined as Amax, Bmax, Cmax and Dmax. The prices of the devices are Ac, Bc, Cc and Dc:
Device  Min amount  Max amount  Price, $ 
A  650  1000  4.5 
B  1700  2200  5.5 
C  1100  1400  6.5 
D  880  1300  7.0 
There are three machines available to produce the devices: M1, M2 and M3. Each machine can operate from Tmin to Tmax minutes:
Machine \ Time  Tmin, min  Tmax, min 
M1  55000  65000 
M2  60000  69000 
M3  62000  68000 
The time required to produce each devices on each machine (T) are given in the table (in minutes):
Machine \ Device  A  B  C  D 
M1  10  12  8  18 
M2  14  11  10  17 
M3  13  10  11  20 
So, time to produce device A on machine M1 is denote
as T_A_M1 and so on. The amounts of devices are required to be found that
maximize the profit. The decision variables are amount of devices
of each type: Ax, Bx, Cx and Dx.
The objective function is sum of multiplications of devices amounts and their costs:
F = Ax * Ac + Bx * Bc + Cx * Cc + Dx * Dc
There are several constraints:
T_A_M1 * Ax + T_B_M1 * Bx + T_C_M1 * Cx + T_D_M1 * Dx >= Tmin for M1 T_A_M1
* Ax + T_B_M1 * Bx + T_C_M1 * Cx + T_D_M1 * Dx <= Tmax for M1 and etc. The problem
has been solved successfully with the following plan:
Device  Amount 
A  650 
B  2200 
C  1400 
D  1107 
The Total Profit is $31877.5
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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