Linear Programming Problem (LPP) Learnig Example with more than 2 varibles For Data Science Biggner in Python and Jupyter

In this Post we will learn lot of Linear Programming Problem Example. I will try to provide the coding part of problem not the lengthy documentation.

Now lets Start with our Examples which is generally asked in various unveristy exams also.

Example 1:-

A Manufacturing compamy is engaged in producing three types of product L, M and  N. The production department produces, each day, components sufficent to make 50 units of L, 25 Units of M and 30 units of N.
The management is confronted with the problem of optimizing the daily production of the prodccts in the assembly department, where only 100 man hours are availble daily for assembly the products.

Following addtional information is available-

Type of Product	Profit Contribution per Unit of Products (RS.)	Assemble Time per product (hrs)
L	12	0.8
M	20	1.7
N	45	2.5

The Company has a daily order commitment for 20 units of product L  and a total of 15 units of M and N.

Now we have to Formulate the  Linear programming model as maximize the total profit.

Now LP Model formulation of the is problem is -

Constraints	Product Type			Total
	L	M	N
Production Capacity	50	25	30
Man Hours per Unit	0.8	1.7	2.5	100
Order commitment	20	15( both of M and N)
Profit Contribution	12	20	45

Maximize Or Objective Function above Problem is -  

     Z=12 X1 + 20 X2 + 45 X3 or 

    Z=12x+20y+24z

Comstraints-

   (A) 0.8X1 + 1.7X2 +2.5 X3 <=100

   (B) X1 <= 50

   (C) X2 <= 25

   (D) X3 <= 30

ORDER COMMITMENT

  (A) X1 >= 20

  (B) X2 + X3 >=15

  (C) X1, X2, X3 >=0

This is the Complete description of our Problem, Now lets start the coding in python to get the final output of problem.

Solution -
As per our profit contribution we should have minimum production of product L, then M and maximum of N.
Now we have to find the coordinates.
1- X1=(0,20) and (0,50)
2- X2= (0,15)
3- X3= (0,15)