Finding Maximum and Minimum value of a function within a specified domain

I have a function which has two independent variable.... I know the range of both the variable Suppose the equation is in the form z=a+bX+cY+dX^2+eY^2 I know the range of X and Y how to get the max/min value of Z for that particular range what will be the value of X and Y also for that particular value of z ??

Answer 1

[Walter Roberson]

You can use some minor calculus to find the key points. The equation is separable into X and Y components and a constant that does not change where the key points are. Differentiate with respect to X, solve for 0 to find the critical X, likewise for Y. After that, try the 9 combinations of the critical points and the boundary conditions to get all the min and max over the ranges