maximum monthly revenue?
On a certain route, an airline carries 7000 passengers per month, each paying $150. A market survey indicates that for each $1 decrease in the ticket price, the airline will gain 50 passengers.
**I've found:
the number of passengers per month, N, as a function of the ticket price, x:
N(x) = 7000+50(150-x)
= 15400-50x
monthly revenue for the route, R, as a function of the ticket price, x:
R(x) = (14500-50x)x
= 14500-50x^2
**How do I find the maximum monthly revenue?
Comments
N(x) = 7000 + 50*(150 - x)
N(x) = 7000 + 7500 - 50*x
N(x) = 14500 - 50*x
R(x) = (14500 - 50*x)*x
R(x) = 14500*x - 50*x^2
**How do I find the maximum monthly revenue?
diff(14500*x - 50*x^2, x) = 14500 - 100*x
solve(14500 - 100*x = 0)
x = 150$, ticket price
R(x) = 14500*x - 50*x^2
R(150) = 14500*150 - 50*150^2
R(150) = $1,050,000, maximum monthly revenue!