function [] = chap_4_prob_33()
% 
% Written by:
% -- 
% John L. Weatherwax                2007-04-02
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

close all; 

b      = 1:15;
lb     = length(b); 

% calculate the pdf we are integrating against:
nRange = 0:10; 
px = binopdf( nRange, 10, 1/3 );

Ep     = zeros(1,lb);
for bi=1:lb,
  % calculate the function "min(n,b)":
  fb = min( nRange, b(bi) );

  % compute the expected profit:
  Ep(bi) = -10*b(bi) + 15*dot( fb, px );
end

figure; plot( b, Ep, '-o' ); 
%axis( [ 0 1 0 1.25 ] ); 
xlabel( 'b' ); ylabel( 'expected profit' ); grid on; 
%saveas( gcf, '../WriteUp/Graphics/chap_4_prob_33.eps', 'epsc' );

[epMax,epIndx] = max( Ep );
fprintf('The max expected profit is %f; by ordering b=%d papers\n',epMax,epIndx);