What is a mathematical expression in linear programming that maximizes or minimizes some quantity?

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Problem:

I am new and my logic is not so strong can any one give me right mathematical expression in linear programming?
What is a mathematical expression in linear programming that maximizes or minimizes some quantity?

Solution:

Objective function in mathematical expression in linear programming that maximizes or minimizes some quantity.
Explanation:

Maximize Z=2x+3y

constraints  x+y<3, x>0, y>0

Maximum Z=2*0+3*4=12

The maximum value of Z is at point B(0,3).

Similarly in this problem, if we take the objective function

Minimize Z=2x+3y using the same constraint the minimum value of Z at corner point O(0,0).

Minimize Z=0

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