# Solving word problems using derivatives

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• Jan 6th 2013, 12:20 PM
MarkFL
Re: Solving word problems using derivatives
Here is a plot of the revenue function for problem 1:

Attachment 26493
• Jan 6th 2013, 12:29 PM
ktkeiper
Re: Solving word problems using derivatives
Yes, thank you. I managed to finish that one. I got 250 passengers. Which seems much more reasonable than my first answer of 15000...
• Jan 6th 2013, 12:42 PM
MarkFL
Re: Solving word problems using derivatives
How did you get 250 passengers? What is the revenue function at x = 250?
• Jan 6th 2013, 12:42 PM
ktkeiper
Re: Solving word problems using derivatives
Okay, I understand that I need to substitute x^2 in for y, but in what? In the distance formula?
• Jan 6th 2013, 01:05 PM
ktkeiper
Re: Solving word problems using derivatives
The problem said to find the number of passengers, not the greatest revenue.
• Jan 6th 2013, 02:14 PM
skeeter
Re: Solving word problems using derivatives
Quote:

Originally Posted by ktkeiper
The problem said to find the number of passengers, not the greatest revenue.

Quote:

A chartering company will provide a plane for a fare of \$300 per person for 100 or fewer passengers (but more than 60 passengers.) For each passenger over 100, the fare is decreased \$2 per person for everyone. What number of passengers would provide the greatest revenue?
fyi, at x = 250 passengers, revenue = 0
• Jan 6th 2013, 04:46 PM
ktkeiper
Re: Solving word problems using derivatives
What formula did you use? Because with my formula, the revenue came out to \$62500
• Jan 6th 2013, 04:55 PM
skeeter
Re: Solving word problems using derivatives
Quote:

Originally Posted by ktkeiper
What formula did you use? Because with my formula, the revenue came out to \$62500

for $x > 100$ ...

$R = x(500-2x)$
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