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# Price vs. Capacity Problem

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On an air rout, an ailine offers two classes of service: busienss (B) and economy (E).
The respective demands are given by:
For B - P= 540-.5Q
For E - P= 380-.25Q

Because of ticketing restrictions business travelers cannot take advantage of economy's low fare. The airline operates two flights daily. Each Flight has a capacity of 200 passengers. The cost per flight is \$20,000.

a- How would the airline maximize the total revenue it obtains from the two flights.

b-What fares should the airline charge and how many passengers will buy tickets of each type? Keeping in mind that max revenue is obtained by setting MRb=MRe

c-Suppose the airline is conserving promoting a single "value fare" to all passengers on this route. Find the optimal single fare using spreadsheet optimizer.

https://brainmass.com/economics/microeconomics/price-versus-capacity-problem-139792

#### Solution Preview

Optimal Revenue, Price vs. Capacity Problem
On an air rout, an ailine offers two classes of service: busienss (B) and economy (E).
The respective demands are given by:
For B - P= 540-.5Q
For E - P= 380-.25Q

Because of ticketing restrictions business travelers cannot take advantage of economy's low fare. The airline operates two flights daily. Each Flight has a capacity of 200 passengers. The cost per flight is \$20,000.

a- How would the airline maximize the total revenue it obtains from the two flights.

Solution:

Given,
For B - P= 540-.5Q
For E - P =380-.25Q

P = 540 - 0.5(Qb + Qe)
TRb= PQb = 540Qb - 0.5Qb2 - 0.5QbQe

Total revenue will be maximum from the business class when d (TRb) / dQb = 0
d (TRb) / dQb = 540 - Qb - 0.5Qe = 0
540 = Qb + 0.5Qe ------------- (1)
...

#### Solution Summary

A price versus capacity problem is depicted.

\$2.49