Question

Info given:

"Problem 1

An airline operates two flights, one light from San Francisco to Denver and another from Denver to St. Louis. The capacity on the first flight is 100 and the capacity on the other is 120. The ODF's, fares and expected demand are as follows:

ODF		Fare	Demand
1	San Francisco to Denver, full fare	150	30
2	San Francisco to Denver, discount	100	60
3	Denver to St. Louis, full fare	120	20
4	Denver to St. Louis, discount	80	80
5	San Francisco to St. Louis, full fare	250	30
6	San Francisco to St. Louis, discount	225	20

"

Task:

"1. Write down and solve the deterministic linear program corresponding to this network. Report the optimal primal and dual solutions."

Answer 1

To write the determinstic LP first we need to identify the objective function of the given problem . Here is objective function is maximize the revenue of the airline . Let are the variable assign to each ODF . And capacity of first flight is 100 and for second is 120

Now LP is as follow

objective

Subject to    ( here we take because its origin palce is same )