Question

The campus bookstore has estimated that it's profit (in dollars) from selling x hundred basketball conference championship t-shirts is given by the equation shown below.

p=-40x^2+581x-520

The demand is currently 500 t-shirts, but euphoria over the championship is subsiding so the demand is dropping by 100 t-shirts per day. how is the profit changing with respect to time?
$____per day

Answer 1

-$80

Explanation:

Assuming that the variation in the number of shirts per day is -1 hundred shirs, the variation in profit with respect to time is given by the derivate of the profit equation:

`p=-40x^2+581x-520\\(dp)/(dx)=-80x+581`

Let x be the number of shirts sold in a day, then x-1 is the number of shirts sold in the following day, the change in profit is:

`p'(x) - p'(x-1)=-80x+581 - (-80(x-1)+581)\\p'(x) - p'(x-1)=-80(x-x+1) = -80`

The profit is changing by -$80 per day.