P(x) = –x2 + 90x – 300 is a profit function where x is the number of items sold, and P(x) is the profit from that sale. Find the maximum profit and the number of items that must be sold to reach that profit.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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P(x) = –x2 + 90x – 300 is a profit function where x is the number of items sold, and P(x) is the profit
from that sale. Find the maximum profit and the number of items that must be sold to reach that
profit. 

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