12th grade calculus
posted by dt .
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?

Let x be the number on the tour
Profit = Revenue  Cost
x[200  2(x50)]  6000  32x
50 > x > 80
For maximum profit,
dP/dx = 200  4x + 100 32 = 0
4x = 268
x = 67 
Let x be the number on the tour
Profit = Revenue  Cost
x[200  2(x50)]  (6000 + 32x)
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