Final answer:
An isocost line represents combinations of inputs for a given cost in microeconomics. For a minimization problem, decreasing costs are illustrated by the isocost line moving down and to the right, not to the left; therefore, the statement is False.
Step-by-step explanation:
In a minimization problem within the context of production theory or microeconomics, it is False that an isocost line slides down and to the left through a feasible region to reflect decreasing costs. Instead, the movement of an isocost line down and to the right reflects decreasing costs.
An isocost line represents all combinations of inputs that a firm can purchase for a given total cost. When trying to minimize costs, a firm will try to reach the lowest isocost line while still remaining within the feasible region set by the isoquant, which represents all input combinations that can produce a given level of output.
As costs decrease, the isocost line moves to a position where it is tangent to a lower isoquant, indicating a lower level of cost for the same level of output. In graphical terms, this movement would typically be down and to the right, not down and to the left.