Question

The electricity supply cables of the three houses shown are connected to a pole as shown. Write a MATLAB program that determines the location of the pole (distance x) that minimizes the total length of the cables needed. In the program define a vector x with values ranging from 50 to 200 with increments of 0.1. Use this vector to calculate the corresponding values of total length of the cables. Then use MATLAB's built-in function min to find the value of x that corresponds to the shortest length of cables.

Answer 1

Matlab code:

x=[50:0.1:200];
total_length=[];
for i=x
total_length=[total_length i+2*sqrt(80^2+(210-i).^2)];
%leaving x the other two cables have same length so 2*sqrt(80^2+(210-i).^2
%sqrt(80^2+(210-i).^2) this is hypotenuse which can be calculated by
%pythagorean theorem
end
min_length=min(total_length);
disp('Minimum total length of cables(in ft.):');
disp(min_length);
index=find(total_length==min_length);
min_x=x(index);
disp('value of x for the length of cables to be minimum is(in ft.):');
disp(min_x);

Output:

null