% Problem:
%Consider the following two formulas.  
%(a) 	A = x*y^2 - 5;
%(b)	B = (x+y)*pi
%Now we require the sum of A and B is 500 and we know that 1 ? y ? 10, 
%please calculate the value of x which can maximize A*B. 

%solution
y = [1:0.1:10];  % create y vector, within 1 and 10 with step 0.1

%sum of A and B is fixed 500
sum = 500;

%sum = x*y^2 - 5 + (x+y)*pi
%    = x*(y^2 + pi) + y*pi
%so, 
x = (sum - y.*pi) ./ (y.^2 + pi)

%now we calculate the product
product = (x.*y.^2 - 5).*((x+y).*pi)

%remember product, as well as x and y, is a vector
%now we find the max product
%as before, z is the max value and k is the index
[z, k] = max(product)

%prepare the final result
%format: x, y, max_product
T = [x(k), y(k), product(k)]