The objective of this exercise is to use MATLAB to find the minimum value of a f

Question

The objective of this exercise is to use MATLAB to find the minimum value of a function. A pipe is to supply water to 4 cities forming a unit square (1 can represent any distance - e.g. 100 miles). The water source is at one of the cities. The goal is to connect the 4 cities with sections of pipe in a way w'hich minimizes the total pipe length. Any number of pipe sections can be joined. The diagrams below show 4 possible configurations. Clearly solution (c), with a 4 way junction, uses less pipe than (a) or (b). The task will be to determine if solution (d) can further reduce the total pipe length.

Explanation / Answer

we can use shortest path algorithm any how to connect 4 cities for the first two case length is 3 which is however smaller than the third case c)2.828

d) l=4x+b

2.828+0=2.828 or in any case if it is less then 1 it ranges between 2.828 and in any case b will be less than 1 because 2a+b=1

so b=1-2a

so any how value ranges between 2

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