Posted by **dt** on Tuesday, November 18, 2008 at 10:56pm.

your operate a tour service that offers the following rate:

$200 per person if 50 people (the minimum number to book the tour) go on the tour

for each additional person, up to a maximum of 80 people total, the rate per person is reduced by $2

it cost $6000 (a fixed cost) plus $32 per person to conduct the tour. how many people does it take to maximize your profit?

- 12th grade calculus -
**drwls**, Tuesday, November 18, 2008 at 11:44pm
Let x be the number on the tour

Profit = Revenue - Cost

x[200 - 2(x-50)] - 6000 - 32x

50 > x > 80

For maximum profit,

dP/dx = 200 - 4x + 100 -32 = 0

4x = 268

x = 67

- 12th grade calculus -
**Anonymous**, Sunday, January 18, 2009 at 3:42pm
Let x be the number on the tour

Profit = Revenue - Cost

x[200 - 2(x-50)] - (6000 + 32x)

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