Question

develop your own original product mix LP problem with two constraints into real variables follow the four steps to formulating LP problems explain the meaning of the numbers on the right hand side of each of your constraints also explain the significance of the technological coefficient.

Answer 1

ANSWER:

Solve following LPP problem by graphical method.

Following is cost problem. Being cost factor, this problem we have to minimize it. There are total 4 cost constraints . Lets say resource cost constraints .

Minimize z =80X+120Y (Cost minimization )

Subject to X+Y<=9 (Material cost constraint )

X>=2 (Machine cost constraint )

Y>=3 (Man cost constraint )

20X+50Y<=300 (Market cost constraint )

X,Y >=0

Answer

Constraint Lines

For X+Y =9

By putting X & Y = 0 alternatively ,

The value will be (X,Y ) =( 9 , 9)

For X = 2

The value will be (X,Y ) =( 2,0)

For X = 3

The value will be (X,Y ) =( 0,3)

For 20X+50Y =300

By putting X & Y = 0 alternatively ,

The value will be (X,Y ) =( 15 ,6)

Vertex Lines Through Vertex Value of Objective

(6,3) x+y = 9; y = 3 840

(5,4) x+y = 9; 20x+50y = 300 880

(2,3) x = 2; y = 3 520 Minimum

(2,5.2) x = 2; 20x+50y = 300 784

Select - 520 Region

Here the concept Technology Coefficients originates from Economics . Its also called as Input Output coefficient. LPP concept is total dependent on the Input & Output concept. Here we are dividing the problem in to two types .

Objective Type
Constraint Type
Now the problem may be of profit or cost , its totally dependent on constraints. They are directly related with each other . So the significant o f this coefficient is that when we want to increase the profit or when we want to decrease the cost we must have strong control on constraints in the system. That is signified by above concept.