# Optimization Travel Agency

• May 16th 2010, 10:27 AM
apocalyps3
Optimization Travel Agency
A travel agent currently has 80 people signed up for a tour. The price of a ticket is \$5000 per person. The agency has chartered a plane seating 150 people at a cost of \$250 000. Additional costs to the agency are incidental fees of \$300 per person. For each \$30 that the price is lowered, one new person will sign up. How much should the price per person be lowered to maximize the profit for the agency?

What I have done;

d(x) = 5000 - 30x
p(x) = 80 + x
R(x) = (5000-30x)(80+x)
R'(x) = 2600 - 60x
x = 130/3

The price that should be lowered per person is 30(130/3) = 1300,

so can anyone tell me what i am doing wrong? Thanks
• May 16th 2010, 11:44 AM
earboth
Quote:

Originally Posted by apocalyps3
A travel agent currently has 80 people signed up for a tour. The price of a ticket is \$5000 per person. The agency has chartered a plane seating 150 people at a cost of \$250 000. Additional costs to the agency are incidental fees of \$300 per person. For each \$30 that the price is lowered, one new person will sign up. How much should the price per person be lowered to maximize the profit for the agency?

What I have done;

d(x) = 5000 - 30x
p(x) = 80 + x
R(x) = (5000-30x)(80+x)
R'(x) = 2600 - 60x
x = 130/3

The price that should be lowered per person is 30(130/3) = 1300,