In a linear programming problem, if are source is not fully utilized, the shadow price of that resource is

The correct option is zero.

In linear programming, a resource constraint is typically represented in the form:
$$a_{i1}{x}_1+a_{i2}{x}_2+...+a_{in}{x}_n\le b_i$$
where $b_i$ is the total available amount of resource i.

If a resource is not fully utilized at the optimal solution, it means that the actual usage of this resource is strictly less than the available capacity. In other words, there is leftover capacity, which is represented by a positive slack variable ($s_i>0$). This indicates that the constraint is non-binding.

The shadow price of a resource is defined as the rate of change in the optimal objective function value per unit increase in the availability of that resource.
Since the resource is already underutilized (non-binding), acquiring more of it will not help improve the objective function value because the system does not even use the amount it currently has. Consequently, the marginal value or economic worth (shadow price) of an additional unit of this surplus resource is exactly zero.