Qunatitative Methods

LINEAR PROGRAMMING
Some examples The simplex method Matrix verbalism Sensitivity analysis Duality theory

 spokesperson 1: mesh maximization
The firm Hikea produces four fibers of cupboards. Producing one cupboard requires some wintry processing time in two departments (hours/unit).

Question: How many a(prenominal) cupboards of each type should be produced by the firm if its documentary is to maximize its total do good?

 model process
Situation ? Modeling, entropy collection, ... ? Model

? Weaknesses ?
Implementation of decisions REAL WORLD ? recital ?

? Solution ?
Conclusions of the model

INTERFACE

MATHEMATICS

Example 1: data collection
A1 Joinery 4 A2 9 A3 7 A4 1 Available hours 6 000

Packaging
Profit/unit (euro/unit)???

1
12

1
20

3
18

4
10

4 000

A mathematical model
Decision variables: xi = number of cupboards of type i produced, i = 1,2,3,4.



Objective function (to be maximized):

profit = z = 12 x1 + 20 x2 + 18 x3 + 10 x4

A mathematical model
Objective function (to be maximized): profit = z = 12 x1 + 20 x2 + 18 x3 + 10 x4

Constraints:
4 x1 + 9 x2 + 7 x3 + x4 ? 6000 x1 + x2 + 3 x3 + 4 x4 ? 4000 x1, x2, x3, x4 ? 0

Optimal solution (computed by Excel)
x1 = 4000/3 = 1333,3 x2 = x3 = 0 x4 = 2000/3 = 666,7 z = 22666,7 These values foregather all the constraints and no other feasible values would fruit a higher value of the objective function z.

Modeling process
Situation ? Modeling, data collection, ... ? Model

? Weaknesses ?
Implementation of decisions REAL WORLD ? Interpretation ?

? Solution ?
Conclusions of the model

INTERFACE

MATHEMATICS

Optimal solution
x1 = 4000/3 = 1333,3 x2 = x3 = 0 x4 = 2000/3 = 666,7 z = 22666,7 Is this an acceptable solution? Should we modify the model?

Sensitivity analysis
allow us impose for instance: - at least vitamin D cupboards of type A1 and A4 - at least 100 cupboards of type A2 and A3. How does this fall upon the previous optimal solution?...If you want to get a full essay, order it on our website: Orderessay



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