YLL討論網

微積分題目
不會解,請幫幫忙~先謝了..感激!!!
(抱歉不太會打題目,希望不會看不懂= =..)
1.
(1)               Is the following function concave or convex?
                       f(x,y)= [(x-1)^A][(y-2)^B]  ,    A,B>0
(2)               Is the above function quasi-concave?
(3)                   If we maximize the above function subject to the constraint  
                   Px+Qy=100,    where  P and Q are parameters.
                   Find the effects of  A and P on the maximal values of f(x,y) ,  respectively.

2.
         The function given in question 1 is now extended to
          f(x,y,z)= [(x-a)^A][(y-2)^B][(z-3)^C]  ,     a,A,B,C>0
(1)              Is the above function concave?
(2)              Suppose that you want to maximize the above function subject to the constraint  
                  x+2y+3z=100.
                  Is the objective function quasi-concave?
(3)             How the maximum value of f(x,y,z) changes as the parameter  ''a''  changes.