Developers from two cities, A and B, want to connect their cities to a major highway and

Question:

Developers from two cities, A and B, want to connect their cities to a major highway and plan to build rest stops and gas stations at the highway entrance. To minimize the cost of road construction, the developers must find the location for the highway entrance that minimizes the total distance, d₁ + d₂, from the cities A and B to the highway. Let x be as in Fig. 18. Find the value of x that solves the developers’ problem, and find the minimum total distance.