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Saul Waters

Feb 20, 2025

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

to book the tour) go on the tour.B. For each additional person, up to a maximum of 80 people total, the rate per person is reduced by $2.It costs $6000 (a fixed amount) plus $32 per person to conduct the tour.How many people does it take to maximize your profit?PLEASE HELP!
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let C(x) be eq. for cost and R(x) be eq. for revenue.C(x) = 6000 + 32(x+50)= 7600 + 32xR(x) = (x+50)(200-2x) = 2(x+50)(100-x)= 10000 + 100x - 2x^2profit, P(x)= R(x) - C(x)= [10000 + 100x - 2x^2] - [7600 + 32x]= 2400 + 68x - 2x^2P'(x) = 68 - 4x = 0x = 68/4 = 17answer :it takes 50+17 = 67 people to maximize my profit of P(17) = $2978.... Show More
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P
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^2differentiate P with respect to x and equate to zerodP/dx = 68 - 4x = 0x = 68/4x = 17therefore the total number of person is N = 50 + x = 50 + 17 = 67... Show More
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P
At 80 people - the profit would be $7,380.At 79 people, the profit would be $7,214. At 78- $7,048 At 77- $6,882At 76- $6,716The answer is 80 people; because as you see the pattern is going down and down.... Show More
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