Saturday

November 22, 2014

November 22, 2014

Posted by **Rob** on Wednesday, March 7, 2007 at 11:25am.

I will be happy to critique your thinking.

- Calc Help -
**Ed**, Wednesday, July 11, 2012 at 8:41pmSince the agency only takes groups of no less than 30 people, the minimum profit for a single trip is $15*30 people.

Let x be the number of people above 30.

The number of people is then 30+x.

The [Total Revenue] is equal to the

[price charged for each person] times the [number of people]

[price charged for each]=$15-.15*x

Notice if x=0, then the price charged is equal to $15 and the number of people in group is 30, which is the minum group size the company will allow for a trip.

Thus our Total Revenue Function is

[Total Revenue] =

[price charged for each person]*[number of people]

=($15-$.15*x)*(30+x)

R(x)= ($15-$.15*x)*(30+x)=450+10.5x-.15*x^2 after foiling everything out.

R'(x)=10.5-2*.15*x is the derivative of the Revenue function and the Revenue will be maximized at a value of x for which R'(x)=0.

Setting R'(x)=0 implies 10.5-2*.15*x=0, which implies that x=35 people. The group size was constrained to be at least 30 people and at most 50 people, and since the number 35 is between 30 and 50, then a group size of 35 people is a valid solution for this problem: according to the revenue function R(x),and the constraints on groups sizes given above above, the company will maximize its profit when it has groups of size 35. Now I must go breath.

**Answer this Question**

**Related Questions**

algebra 2 - A drama club is planning a bus trip to new york city to see a ...

Calculus - A travel agency currently has 80plp signed up a tour. The price of a ...

math - If exactly 198 people sign up for a charter flight, Leisure World Travel ...

math - If exactly 198 people sign up for a charter flight, Leisure World Travel ...

Math - If exactly 198 people sign up for a charter flight, Leisure World Travel ...

Mathematics - A travel agency offers group tours at a rate of $60/person for the...

Algebra - A catering company charges a $300.00 set up fee and $10.00 per person ...

maths - The insight bus tour offered to take a group of senior citizen to a lake...

maths - The insight bus tour offered to take a group of senior citizen to a lake...

math - information: (C)Charges $750 for up to 30 people. (P)Plus $20 per person ...