Thread: 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,
but the answer is 1140

so can anyone tell me what i am doing wrong? Thanks

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,
but the answer is 1140

so can anyone tell me what i am doing wrong? Thanks

According to the highlighted condition your function R becomes:

R(x) = (5000-30x)(80+x)-300x

Keep in mind that the number of passengers must be a natural number!