In both cases, the gradient vector is always perpendicular to the level curves. For maximization, it points in the direction of increasing objective value (higher profit), while for minimization, optimization requires moving in the exact opposite direction of the gradient toward lower cost.

The gradient is perpendicular to the level curves and points toward increasing values for maximization, while for minimization it points toward decreasing cost values.

The gradient points perpendicular to the level curves: for maximization it points toward increasing profit, while for minimization it points toward decreasing cost.

The gradient is perpendicular to the level curves in both cases, but for maximization it points toward increasing profit, while for minimization it points toward increasing cost, so the optimal search direction is opposite the gradient.

The gradient vector always points perpendicular to the level curves, whether they represent iso-profit or iso-cost lines, directly toward the direction of increasing function values. In a maximization problem, the gradient vector points toward higher profit levels, guiding the search algorithm outward in the direction of the vector toward the peak of the feasible region. Conversely, in a minimization problem, the gradient vector also points toward increasing cost values, but the algorithm must move in the exact opposite direction of the vector to descend backward along the perpendicular path toward the lowest valley where cost is minimized.

How does the direction of the gradient vector differ between maximizing profit and minimizing cost when analyzing their respective level curves?