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Linear Programming Production (profit maximization) problem

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linear programming GIPALS Start

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 GIPALS Start

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.

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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