May be graph theory. Cities connected by airlines

Question

There are 175 cities and two airline companies in a certain country. By airlines of each airline company you can get from any city to any other city. The cost of a direct flight between two cities is $2\$$ if they are connected by a single direct airline and $1\$$ if they are connected by two direct airlines.

You want to get from city A to city B and you chose route with the lowest price.

What is the largest amount you may need for this trip?

I think the answer is $232=4+4(175-4)/3$ but I don't know how to prove it.In the example below the highest price is 4\$ between $A$ and $D$.

$A$ and $D$, green lines represent airlines of company 1 and red lines represent airlines of company 2" />

Let cities are $A_1,A_2,...,A_{175}$ for any pair $A_iA_j$ let $min_{ij}$ be the lowest price between $A_i and A_j$, we are looking for configuration when $Max{min_{ij}$ is as large as possible.