production of a commodity in three different factories is as under.present it through suitable diagram
factory P,Q,R
production 256,576,1024
Answers
Answer:
Formulation of Linear Programming Model:
Step-1:
From the study of the situation find the key decision to be made.In this connection,looking for variables helps considerably.In the given situation key decision is to decide the number of units of products
1,2and3
to be produced daily.
Step-2:
Assume symbols for variable quantities noticed in step-1.Let the number of units of products,
1,2,and3manufactured daily be
2
x
1
and
x
3
.
Step-3:Express the feasible alternatives mathematically in terms of variables.Feasible alternatives are those which are physically,economically and financially possible.In the given situation feasible alternatives are sets of values of
2
x
1
and
x
3
.
where
2
3
x
1
0
.
since negative production has no meaning and is not feasible.
Step-4:Mention the objective quantitatively and express it as a linear function of variables.In the present situation,objective is to maximize and profit.
i.e.,maximize
Z=
4x
1
+
3x
2
+
6x
3
Step-5:Put into words the influencing factors or constraints.These occur generally because of constraints on availability(resources) or requirements(demands).Express these constraints also as linear equations/inequalities in terms of variables.
Here,constraints are on the machine capacities and can be mathematically expressed as
2x
1
+
3x
2
+
2x
3
≤
440
4x
1
+
0.x
2
+
3x
3
≤
470
2x
1
+
5x
2
+
0.x
3
≤
430
∴
,
the complete mathematical(L.P) model for the problem can be written as
Maximize
Z=
4x
1
+
3x
2
+
6x
3
subject to constraints,
2x
1
+
3x
2
+
2x
3
≤
440
4x
1
+
3x
3
≤
470
2x
1
+
5x
2
≤
430