Begin by carefully rereading the problem statement to ensure a complete understanding of what is being asked and what constraints are in place.
Double-check that the objective function accurately represents the quantity you are trying to maximize or minimize, and that all variables are appropriately defined.
Ensure that all constraints are expressed as mathematical inequalities or equalities that precisely reflect the limitations given in the problem.
Graph the constraints, if possible, to visually confirm the feasible region, or test points within and outside the region to verify they satisfy the constraints.
Substitute the critical points back into the objective function and constraints to confirm they satisfy all conditions and yield a potential maximum or minimum value.
Check the endpoints of the feasible region and any points where the derivative is undefined, in addition to the critical points found within the region.
Verifying that the units of all terms in the objective function and constraints are consistent helps prevent errors and ensures the solution is physically meaningful.
Use graphing calculators or mathematical software to graph the functions, solve equations, and check the validity of your solution against the problems conditions.
Review your solution in the context of the original problem to ensure it makes logical sense and aligns with expected outcomes, considering practical limitations.