You operate a tour service that offers the following rates:A $200 per person if 50 people (the minimum number?

Question

You operate a tour service that offers the following rates: A base rate of $200 per person applies when a minimum of 50 people book the tour. For every additional person, up to a maximum of 80 participants, the rate per person decreases by $2. The fixed costs to conduct the tour total $6,000, along with an additional variable cost of $32 per person. How many participants are required to maximize your profit? Please help!

Anonymous · Accepted Answer

let C(x) be eq. for cost and R(x) be eq. for revenue.

C(x) = 6000 + 32(x+50)

= 7600 + 32x

R(x) = (x+50)(200-2x)

= 2(x+50)(100-x)

= 10000 + 100x - 2x^2

profit, P(x)

= R(x) - C(x)

= [10000 + 100x - 2x^2] - [7600 + 32x]

= 2400 + 68x - 2x^2

P'(x) = 68 - 4x = 0

x = 68/4 = 17

answer :

it takes 50+17 = 67 people to maximize my profit of P(17) = $2978.

Anonymous · Answer

let x be the number of additional person 
Profit (P) = [(50+x)(200-2x)] - [6000 + 32(50+x)]
            = 10000 - 100x + 200x - 2x^2 - 6000 - 1600 -32x            = 2400 + 68x - 2x^2
differentiate P with respect to x and equate to zero
dP/dx = 68 - 4x = 0
x = 68/4
x = 17
therefore the total number of person is 
N = 50 + x = 50 + 17 = 67

Anonymous · Answer

At 80 people - the profit would be $7,380.
At 79 people, the profit would be $7,214. 
At 78- $7,048 
At 77- $6,882
At 76- $6,716
The answer is 80 people; because as you see the pattern is going down and down.

Anonymous

You operate a tour service that offers the following rates:A $200 per person if 50 people (the minimum number?

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