Question

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?

Answer 1

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

Answer 2

Let x be the number on the tour

Profit = Revenue - Cost
x[200 - 2(x-50)] - (6000 + 32x)