function [res] = chap_5_prob_2_scaled_fn(x, w)
%
% problem on epage 167
% computes the blended functions f_1 and f_2 on epage 117 (scaled and weighted)
% 
% Inputs: 
%   x in N_pop x N_vars of scaled input variables 
% 
% Written by:
% -- 
% John L. Weatherwax                2006-08-28
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

% compute each of the subfunctions f_n: 
% 
Fs = chap_5_prob_2_original_fns(x);
f_1 = Fs(:,1); f_2 = Fs(:,2);

% compute the scaling factors for f_1 and f_2: 
%
f_1_min = 4;
f_1_max = 8 + sqrt(2);
f_2_min = 9/4;
f_2_max = 3 + sqrt(2);

% scale each function so that it has a range of between 0,1
%
f_1 = ( f_1 - f_1_min )/(f_1_max - f_1_min);
f_2 = ( f_2 - f_2_min )/(f_2_max - f_2_min);

% blend the functions with w: 
%
res = w * f_1 + ( 1 - w ) * f_2;