11. on a certain route, an airline carries 9000 passengers per month, each paying $150. a market survey…

11. on a certain route, an airline carries 9000 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.\na. express the number of passengers per month, n, as a function of the ticket price, x.\nb. express the monthly revenue for the route, r, as a function of the ticket price, x.

11. on a certain route, an airline carries 9000 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.\na. express the number of passengers per month, n, as a function of the ticket price, x.\nb. express the monthly revenue for the route, r, as a function of the ticket price, x.

Answer

Explanation:

Step1: Find the number of passengers per month

The initial number of passengers is (9000). The change in price is ((150 - x)) dollars. Since for each ($1) decrease, there are (50) more passengers, the number of passengers (N) is (N=9000 + 50(150 - x)). Simplify: [ \begin{align*} N&=9000+7500 - 50x\ N&=16500-50x \end{align*} ]

Step2: Find the monthly revenue

Revenue (R) is the product of the number of passengers (N) and the ticket price (x). Since (N = 16500-50x), then (R=x\times N). Substitute (N) into the revenue formula: (R=x(16500 - 50x)=16500x-50x^{2})

Answer:

a. (N = 16500-50x) b. (R=16500x - 50x^{2})