The law of diminishing returns states that as more units of a variable input are added to a fixed input, the marginal product of the variable input will eventually decrease. In other words, there comes a point where adding more of a certain input does not result in proportional increases in output.

(a) Reflected in the negatively sloped portion of the marginal product curve:
The law of diminishing returns is reflected in the negatively sloped portion of the marginal product curve. The marginal product curve shows the additional output that is produced when one more unit of the variable input is added, while keeping all other inputs constant. Initially, as more units of the variable input are added, the marginal product increases, resulting in an upward sloping portion of the curve. However, after a certain point, the marginal product starts to decrease, leading to a negatively sloped portion of the curve. This demonstrates the diminishing returns that occur when adding more of the variable input.

(c) Related to increasing coordination problems:
The law of diminishing returns is also related to increasing coordination problems. As more units of a variable input are added, it becomes increasingly difficult to coordinate and manage all the inputs effectively. This can lead to inefficiencies and decreased productivity. For example, if a factory has a fixed amount of space and hires too many workers, they may start to get in each other's way, resulting in coordination problems and a decrease in overall productivity.

(d) Both (a) and (c):
The correct answer is option (d) because the law of diminishing returns is reflected in the negatively sloped portion of the marginal product curve (option a) and is also related to increasing coordination problems (option c). These two aspects are interconnected and demonstrate the concept of diminishing returns as more units of a variable input are added.