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.