The southwest would be the best region to expand into.
Step-by-step explanation:
Step 1; Mr. Sammie has decided to expand his business. To determine which region is best suited for expansion there should be the least number of already existing trucks in that region.
Density = [tex]\frac{mass}{volume}[/tex], here mass is the number of already existing trucks and the area is the area of the region.
Step 2; The densities of the different regions are calculated.
The density of Northwest = [tex]\frac{320}{10,972}[/tex] = 0.0291,
The density of Northeast = [tex]\frac{400}{9,485}[/tex] = 0.04217,
The density of Central = [tex]\frac{480}{11,645}[/tex] = 0.04121,
The density of Southwest = [tex]\frac{515}{11,589}[/tex] = 0.0444,
The density of Southeast = [tex]\frac{250}{9,933}[/tex] = 0.0251.
Step 3; If we reciprocate the density, we can calculate the number of miles each truck has to itself.
Northwest = [tex]\frac{1}{0.0291}[/tex] = 34.3642,
Northeast = [tex]\frac{1}{0.04217}[/tex] = 23.7135,
Central = [tex]\frac{1}{0.04121}[/tex] = 24.2659,
Southwest = [tex]\frac{1}{0.0444}[/tex] = 22.522,
Southeast = [tex]\frac{1}{0.0251}[/tex] = 39.840.
So the Southwest region is the best to expand into as it is the least dense.
