Final answer:
The student's linear programming problem has a feasible region (option c) where the objective function 2X1 + 3X2 can be maximized subject to the constraints.
Step-by-step explanation:
The student's question relates to maximizing an objective function subject to given constraints, which is a problem often encountered in linear programming, a topic within the field of mathematics.
To address the student's query about maximizing 2X1 + 3X2, given the constraints X1 + X2 ≤ 4, X1 ≥ 2, and X1, X2 ≥ 0, we note that this linear programming model has a feasible region defined by the intersection of half-planes created by each constraint. Since there are constraints present, we can disregard options a) and d). The constraints X1 ≥ 2 and X1, X2 ≥ 0 ensure that the solution must lie in a region that is at least feasible, eliminating option b).
Therefore, the correct choice is c) A feasible region, where the values of X1 and X2 within this region represent all the possible solutions to the linear programming problem, and the maximal value of the objective function corresponds to one of the vertices of the feasible region.