Final answer:
The interval of interest of the objective function is determined by Mathematical constraints. These are the conditions dictating the feasible region within which the optimal solution of the function must reside, such as inequalities and domain restrictions specific to the mathematical problem.
Step-by-step explanation:
The interval of interest of the objective function is determined by B. Mathematical constraints. The objective function's interval is not typically influenced by personal preference, cultural factors, or historical events, but rather it is defined by the mathematical problem itself.
This interval can be influenced by factors such as the domain and range of the function, or any restrictions that come into play based on the context of the problem or system being analyzed.
In the realm of optimization, where an objective function is usually maximized or minimized, the feasible region—dictated by the mathematical constraints—is where you'll find the interval of interest for the function. These constraints can be inclusive of boundaries, inequalities, or other mathematical conditions that define the scope within which the optimal solution must be found.
For example, in a linear programming problem, the mathematical constraints are the set of inequalities or equations that define the feasible region. The interval of interest with respect to the objective function would be within this feasible region, and it is usually the corners or edges of this region (depending on whether it's a maximum or minimum problem) that provide the optimal solution.
Therefore answer is B. Mathematical constraints.