2. A travel agency sells group tours to South America. The agency is selling tic
ID: 2888330 • Letter: 2
Question
2. A travel agency sells group tours to South America. The agency is selling tickets for a group of size x total people at p =-10x + 950 dollars per person. The average cost +250 dollars per person (a) Find and simplify the Total Profit function, P(x) (b) What size of group will maximize the agency's profit? Support your answer with clearly organized calculus. (c) What is the maximum profit for such a tour? (d) What is the per person price of the tour at the maximum proft level? Show how you calculate this.Explanation / Answer
2)
given average cost = (3000/x) +250
total cost ,C(x)=x*((3000/x) +250)
C(x)=3000 +250x
revenue ,R(x)= x*(-10x+950)
R(x)= -10x2+950x
(a)
total profit,P(x)=R(x) -C(x)
P(x)=(-10x2+950x) -(3000+250x)
P(x)=-10x2+950x -3000-250x
P(x)=-10x2+700x -3000
(b)
P'(x)=-20x+700
P"(x)=-20
for critical point ,P'(x) =0
=>-20x+700=0
=>x=700/20
=>x=35
P"(35)=-20 <0
group of 35 will maximize the agency's profit
(c)
maximum profit = P(35)
maximum profit = -10(35)2+700(35) -3000
maximum profit = 9250 dollars
(d)
per person price at maximum profit level=(3000/35) +250
per person price at maximum profit level=335.71 dollars
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