s1rout2.m

Industrial Mathematics

% Routine 1.2
n = 5000;                          % number of potential customers
p = 100/n;                         % probability of a sale                                                                                                                 clear E;                           % clear the variable E
for m=85:105                       % experiment with number of papers bought
  pk= (1-p)^n;                     % initialize p(0)
  e = -.5*m*pk;                    % (profit) with no sales 
  for k=1:m                        % sum expected profit for k <= m
    pk = ((n-k+1)*p)*pk/((1-p)*k); % p(k) is obtained from p(k-1)
    e = e + (.75*k - .5*m)*pk;     % add in profit from selling k-th paper
   end;                            % finish summing for k <= m
  for k=m+1:n                      %  sum expected profit for k > m
    pk = ((n-k+1)*p)*pk/((1-p)*k); % p(k) is obtained from p(k-1)
    e = e +  .25*m*pk;             % add in profit from selling k-th paper
   end;                            % finish summing profit; 
E(m)= e;                           % tabulate profit e when buying m papers 
end  
plot(E)