The most fitting response to the question about how the map helps develop the central idea that the Louisiana Purchase had profound effects on sugar and the United States is:
The map illustrates the size of the Louisiana Purchase and suggests its economic potential.
This response emphasizes the significance of the vast land acquired through the Louisiana Purchase, which would have implications for sugar cultivation and the overall economy of the United States. The size of the territory indicates the potential for agricultural expansion, including the establishment of sugar plantations that could arise following the Haitian Revolution.