emmak wrote:
For a particular company, the profit P generated by selling Q units of a certain product is given by the formula P = 128 + (–Q2/4 + 4Q – 16)^z, where z > 0. The maximum profit is achieved when Q =
(A) 2
(B) 4
(C) 8
(D) 16
(E) 32
The answer will be [C], but I believe it will hold for only odd values of z.
The above expression can be reduced to P = 128 + {[Q^2 -16Q + 64]/2}^z *(-1)^z
=> 128+ [Q-8/2]^2z * (-1)^z
for all values of z, [Q-8/2]^2z will be an increasing function with its minima at 8. Also, for odd values of z (-1)^z = -1, which will be reversing the sign of the same. Hence, for Q=8 and z is odd, the above expression will have a maxima. I am still unsure as to why the z is even part not considered. In such a case, the function will be open and its maxima cannot be determined.
Please correct me if I am wrong and request you to verify my procedure!
Regards,
Arpan