LINEAR PROGRAMMING IN LAYMAN’S TERM
Linear Programming is a mathematical technique and operation that can be used in administrative and economic planning in maximizing the function of bigger and wide range of variables that signifies constrain. This function is widely used for complicated computation of broad spectrum of calculation and precise handling of data processing just like on a high speed computer, it is also used for engineering, design, industrial, military and research operation purpose and experimentation of new products or software development programming. Usually if there are missing links of inputs linear, programming is excellent that supersede the expectation of computation using sets of symbols and formula development of any given problems that needs accurate method or solution.
This computation requires a thorough knowledge and trial and error to highly develop sets of variables in problem solving which is logical to understand that the brainchild of a computer understand and function through this sets of given data that transform into a command to execute from. To be able to fully illustrate such function and maximize its potential we will thoroughly discuss it in layman’s term so that in itself is effective. We are also going to express some example that you may need to re read to fully understand such expression. The easiest method would be to analyze the data and put it on the table you can also use Microsoft excel as shown below or simply create an equation that is according to the situation.
TOY COMPANY
My company can produce a different kinds of toys let us say a Teddy Bear, Rabbit, Panda and Doggy. The minimum number of toys produced per day are TBmin, Rmin,Pmin and Dmin. The maximum numbers are stated as TBmax, Rmax, Pmax and Dmax. The prices of the toys are TBp, Rp, Pp and Dp:
Toys
Min number
Max number
Price, $
TB
100
200
5
R
95
190
6
P
90
180
7.0
D
95
190
7.0
I have used the following machines to produce the toys: M1, M2 and M3. Each machine can operate from Tmin to Tmax hours per day:
Machine \ Time
Tmin, hrs
Tmax, hrs
M1
20
22
M2
20
22
M3
20
22
The time required to produce each toys on each machine (T) are given in the table (in minutes):
Machine \ T
TB
R
P
D
M1
10
12
10
18
M2
10
14
11
19
M3
10
10
12
20
So, time to produce toys TB on machine M1 is denote as T_TB_M1 and so on. The following amounts of toys have been required to maximize the profit. The decision variables are amount of toys of each type: TBx, Rx, Px and Dx.
Although there are several constraint we are going to focus on the following constraints:
T_TB_M1 * TBx + T_R_M1 * Rx + T_P_M1 * Px + T_D_M1 * Dx >= Tmin for M1 T_TB_M1 * TBx + T_R_M1 * Rx + T_P_M1 * Px + T_D_M1 * Dx <= Tmax for M1 and etc.
The objective function is sum of multiplications of devices amounts and their costs: we are going to measure its profitability which is equal to F and c is equal to the cost.
F = TBx * TBc + Rx * Rc + Px * Pc + Dx * Dc
You can now create several questions and formula using the data above. Or using tables you can easily figure out future production and monitor its minimum or maximum output to give simple expression for example.
Let us say I am going to produce a Teddy bear in a minimum amount as ordered by the customer using machine 1 how much would I earn? The formula would be T_TB1_M1 / T_Tmin_M1 X TBp which is equal to 10 / 20 x 5 first we need to convert 20 to minutes which is 60 X 20 since 60 minutes is equal to 1 hour therefore 1200 should be in the final equation would be the following: 10/ 1200 x 5 = 0 dollars will be the minimum earnings using the minimum hours using the machine 1 in this question.
This question has been the simplest question but if you need to compute the maximum amount it would be very easy. You can also add up many constraints depending on the particular production of works involved but the table has been very useful in determining the basic formula. In a more sensitive approach which is the average linear programming the following table can be introduced using graphical interface that can be use for special training or basic presentation but the equation would be the same.
Credit:ivythesis.typepad.com
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