Q Units

[nikhil.baveja]

Hi Saw this Question in MGmat challenge set.

For a particular company, the profit P generated by selling Q units of a certain product is given by the formula P = 128 + (-Q^2/4 + 4Q - 16)^z, where z > 0. The maximum profit is achieved when Q =

(A) 2
(B) 4
(C) 8
(D) 16
(E) 32

Now I understand the way it is solved in MGmat Answer set the explanation was something like this..

P = 128 - ¼(Q^2 - 16Q + 64)

Now factor the quadratic: Q^2 - 16Q + 64 = (Q - 8)^2

So the formula looks like this:

P = 128 - ¼(Q - 8)^2

and then calculating the minimum value as 8.
now here is how I approached the Question when I looked at it and TBH I often misunderstand the concept of these maximum/minimum Questions. It will be appreciated if someone can provide me a source of some reference to basics of maximization or minimization problems.

Anyways, the moment I saw the question stem I realized Q is a negative number but its Q^2 so i need the largest absolute value of Q and since larger the value for Q will be, Larger Q divided by 4 and then add 4Q(again larger Q means larger number to add) and then subs-tract 16 which is constant. and then 128 is added to this whole function. so why do we need to factor it as a quadratic? and moreover why the result is different considering that whatever is in bracket(-Q^2/4 + 4Q - 16)^z will always be a positive number to add to 128 outside the bracket.
It may sound like foolish question, but I need to understand this else I will always repeat the same mistake while handling maximum/minimum problem.

Thanks.
Nikhil

[tim]

the way you approached this problem does not make sense. not only is it not mathematically sound, but your starting point of assuming Q was negative is incorrect and logically impossible. if you want to know how to do this problem, study the official answer to this one. you haven't given any indication why you find the official explanation inadequate, you just seem to be asking for some other resource besides the official explanation. can you help me understand how the official explanation failed to help you so that we can help you here on the forums?