Definition of Mathematical Model
The most important thing in linear programming is to transform the verbal matter into a mathematical model that is a daily language pronunciation into a simpler and easier to understand language of mathematics. So the mathematical model is a formula derived from an interpretation when translating a verbal matter.How To Convert Verbal Sentence To A Mathematical Model In The Form Of Inequality System
To make it easier to change the verbal problems in the form of linear program into the capital mathematics used table as follows:
Example:
To make bread A required 200 grams of flour and 25 grams of butter. As for bread B required 100 grams of flour and 50 grams of butter. The available flour is only 4kg and the butter is 1.2kg. If the price of bread A Rp. 400,00 and bread B cost Rp. 500.00. Make a mathematical model!
Answer:
Suppose a lot of bread A = x and lots of bread B = y, meaning other variables are flour and butter. So the table is obtained as follows:
Flour and butter available at most 4 kg = 4000 grams and 1.2 = 1200 grams so the sign of inequality is "<". From the table can be made inequality as follows:
200x + 100y < 4000, simplified to:
2x + y < 40
25x + 50y < 1200, simplified to:
x + 2y < 48
Since x and y are nonnegative integers then:
x > 0
y > 0
The above four inequalities are requirements that must be met called the constraint function. the price of bread A Rp.500,00 and bread B Rp.400,00, then the sales proceeds can be formulated with Z = 400x + 500. y: Z is called objective function or target function that can be maximized or minimized.
Similarly this article.
Sorry if there is a wrong word.
The end of word wassalamualaikum wr. wb
Referensi :
- To'Ali's book math group accounting and sales
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