Target Function Optimum Value of Regional Linear Inequality System

The important thing in the linear programming problem is to change the problem of variables into the form of mathematical model which is the representation of everyday language into a simpler and easier to understand math language.

Steps to Get Optimum Value

Here are the steps that must be taken to get the optimum value:

1. Convert variable issues into mathematical models.
2. Define Settlement Set.
3. Determine all the corner points in the faesible area.
4. Calculate the value of the objective form for each corner point in the feasible region.
5. From the result in step 4, the maximum or minimum value can be set.

Exmple:

An airplane has a seating capacity of no more than 48 persons. Each main class passenger can carry 60 kg baggage and economy class 20 kg, while the aircraft has a capacity of not more than 1440kg. If the ticket price for the main class and economy are Rp.1.000.000,00 and Rp.500.000,00 per person, determine the number of passengers per class for maximum ticket sales result!

Answer:
The mathematical model is constructed by supposing the number of main class passengers = x people and the number of economy class passengers = y people.

Maximum Z = 1.000.000x + 500.000y

Capacity requirements:
x + y < 48
60x + 20y < 1440
x > 0
y > 0

From the mathematical model in can be OBAC feasible area with point B searched as follows:

x + y = 48
y = 36

then the point B (12, 36)

Test the points of the corner, ie points O, A, B, and C.

The maximum value Z is Rp. 30.000.000,00 is fulfilled by x = 12 and y = 36, or in other words ticket sales will be maximum if number of main class passengers are 12 people and economy class are 36 people.

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Referensi :

• To'Ali's book math group accounting and sales

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