1. The revenue from selling q items is R(q) = 650q-q^2, and the total cost is C(
ID: 2897545 • Letter: 1
Question
1. The revenue from selling q items is R(q) = 650q-q^2, and the total cost is C(q) = 75+14q. Write a function thatgives the total profit earned, and find the quantity which maximizesthe profit.
Profit p(q) =
Quantity maximizing profit q =
2. A tour service offers the following rates:$200 per person if 50 people (the minimum number to book the tour) go on the tour. For each additional person, the rate per person is reduced by $2.It costs $6000 plus $32 per person to conduct the tour. How many people does it take to maximize the profit?
Explanation / Answer
(a) profit= R(q)-C(q)
P(q)=636q-q2-75
Quantity maximizing profit q when P'(q)=0
P'(q)= 636-2q=0
q=318
(b)profit function P(n)= 200*50+ (200*n)-(n*n+1)/2-6000-32*n; where n is additional passengers, n=0,1,2....
so to maximize profit P'(n)=0
200-(2n+1)/2-32=0
therefore n= 167.5
so either 167 person extra or 168
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