Usage of "optimize" [closed]

Solving an optimization problem

max/min corn(X,Y,Z)
(X,Y,Z) in A,

fully, consists in finding two things:

1. Finding the max/min possible value that the function corn can attain under the restriction that (X,Y,Z) is in A.

2. Finding all the points of A for which that maximum/minimum is attained.

Note that once you have the latter, then the optimal values can be obtained by evaluating the objective function. If, on the other hand, you have the optimal values, then the set of optimizing points can be found by solving an equation (inverting the objective function).

In this sense, when you have one, you can produce the other. The problem is essentially solved.

This is why both options, (1) and (2), are used to refer to solving the same problem. One optimizes both the values of the objective function and the values of the variables.