FORMULATION OF L.P.P

                  FORMULATION OF L.P.P

Formulation consists of the following four steps:

Step:1 Identity the variables (which are also called decision variables)

Step:2 write down the objective function to be optimized (maximized or minimized) as a 

linear function of the decision variables after identifying the cost co-efficient.

Step:3 Note down the constraints on the basis of the conditions regarding availability of 

time , demand for the product, etc. constants aij’s and bi’s are involved.

Step:4 Mention the non negative restrictions which imply that the decision variables can 

not be negative.

Example: 1

A company makes three products X, Y and Z which pass through three

Departments: drill, lathe and assembly. The hours available in each department, hours required

By each product in each department and profit contribution of each product are given below:

Time required in hours

 Product Drill Lathe Assembly Profit per unit (Rs)

X 3 3 8 9

Y 6 5 10 15

Z 7 4 12 20

Hours available 210 240 260

Formulate the above as an L.P.P.

Solution:

Decision variables:

Let x1 be the number of units of production of X

x2 be the number of units of production of Y

x3 be the number of units of production of Z.

As the profits per units of X, Y and Z are 9, 15 and 20.

The objective function maximize Z= 9x1+15x2+20x3

The hours available in drill together with the hours required by each product in drill lead to the 

constraints 3x1+6x2+7x3  210

Similarly, from those of lathe and assembly

3x1+5x2+4x3  240 and8x1+10x2+12x3  260

The non negative constraints are x1, x2 and x3 0

Thus, the mathematical formulation of the given L.P.P

Maximize Z= 9x1+15x2+20x3

Subject to constraints

3x1+6x2+7x3  210

3x1+5x2+4x3  240 

8x1+10x2+12x3  260

                     Sanjeevan.m

                      23UCM029

                       I B.com

                      13/2/2024