The selecting of best element among the available alternatives is refereed as the mathematical optimization. If we consider the most simplest case of finding the optimum problem arouse out of function which contains its minimization or maximization of the symmetrical value chosen from the allowed Set after computing the value of the function. A large sector of applied mathematics is used in the formulation of the techniques this is just the generalization of optimum theory. Now let us understand this with the help of the example:
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1. Optimizing the volume and amount of certain 3 – Dimensional figures and other objects in order to lower fabrication budgets. These problems can be solved in 2 – Dimensions also.
To understand such problems let us consider an example: Find out the unknowns i.e. the variables in your equation and Set their values accordingly to write an equation. Optimization of value of one variable is needed to be done in order to get the desired value of another variable.
For Example we have an equation: 2 B = 8 A2 + 12 A,
Separate one of the variables (A and B). We generally consider the variable that lies on y- axis. So, we get:
B = 4 A2 + 6 A,
Next step is to find the derivative of equation we got in previous step as follows:
D(B) /D(A) = 8 A + 6,
Equating the derivative with 0 we get:
0 = 8 A + 6,
On solving above equality we get A = - (3 /4),
Substitute the value of known quantity i.e. A in the original equation to get the corresponding optimized value of B. Thus we are able to find the solution for all the variables in the equation as A = - (3 /4) and B = - (9 /4).