word problems

Question

demand for an overseas tour is q = 250 reservations per month when the tour is priced at p = $2000, and q = 50 reservations per month when it is priced at p = $4000.
a) Find a linear model for demand q = D(p).
b) Find the percentage change in demand when price is raised form $2000 to $2100 (i.e., price rises 5%). Give the value of the ratio E = (% decrease demand)/(% increase price).
c) Find the total revenue as a function of price, R (p).
d) If the price is currently $2000 per tour, will revenue rise or fall if the price is increased to $2100?

Answer 1

(q1, p1) = (250, 2K)

(q2, p2) = (50, 4K) slope

double price and quantity demanded went down by 1/5

q -50 = (-1/10)(p- 4,000)

q = -p/10 +400 +50

q = -p/10 +450

total revenue = R(p) = pq = p(-p/10 +450) = 450p -.1p^2

if price rises from 2000 to 21000 (a 5% increase) by what percent does quantity demanded decrease?

q = 250 when p =2000

q = 240 when p =2100

250 to 240 is a decrease of 10

10/250 = 1/25 = .04 = 4% decrease

R(p)= pq R(2000) = 2000(250) = 500,000

R(2100) = 2100(240) = 504,000

revenue goes up by 4,000 when price goes up $100 from $2000 to $2100