Answer:
(a)
60 thousand dollars
(b)
1 thousand MP3 players
(c)
0 or 2000 MP3 players
Step-by-step explanation:
(a)
We start by finding the derivative, which is -120x+120. We can find this by using the power rule, which has 60x² turn into 2*60*x, and 120x turn into 1*120*1. Finding the stationary points, or when the derivative is 0/when the graph goes from up to down or vice versa, we solve for -120x+120=0, so 120=120x and x=1. Plugging this in, P is 60, and is clearly not a minimum as r(0) = 0, where r is the function. Thus, as this is a local maximum and there is only 1 stationary point, this is the maximum. (a) is then 60.
(b)
This is 1, which has already been established.
(c)
For this, we must find when the profit, or 120x-60x^2, equals 0. We then have 120x-60x^2=0. Dividing both sides by 60x, we get 2-x=0, and x=2. However, this is not the only answer, as there is at least one x in both 120x and 60x^2. Therefore, we must check for 0, and since r(0) is 0, that is a correct answer as well.
