Question

A travel agency currently has 80plp signed up a tour. The price of a ticket is $5000 per person. The agency has chatered a plane seating 150 plp at a cost of $250000. Additional costs to the agency are incidental fees of $300 per person. For each $30 that the price is loverwd, one new perosn will sign up. How much should the price per person be lowered to maximise the profit fo the agency?

Answer 1

P= r - c
p= (5000-30x)(80+x)-300x
p'= -60x + 2300
x = 38.3
therefore 38.3 * 30 = 1150 per person

Answer 2

X additional people
R=(80+x)(5000-30x)
(80+x) is total people
(5000-30x) is ticket price
C=300x + 250 000
P = R - C
P= (80+x)(5000-30x) - (300x + 250 000)
Expand and take derivative
P'= -60x + 2300
X = 38.3
Plug x into ticket change per person
30 × 38.3 = 1149 in ticket cost diff.