a) The Linear Program is as follows:
The objective function is to maximize the total profit
Total Profit =
Decision variables: (Number of passengers of each type in each fare class)
Constraints:
1) Number of people traveling from Istanbul to Ankara and Antalya across all the three fare classes should be less than or equal to 30
and represent the passengers traveling from Istanbul
2) Number of people traveling from Istanbul to Antalya and Ankara to Antalya across all the three fare classes should be less than or equal to 30
represent the passengers traveling from Istanbul to Antalya and represent the passengers traveling from Ankara to Antalya
3) The number of passengers of any type traveling in any fare class should be less than or equal to the upper bound uij
b) The cost of taxes are to be accounted
We introduce a variable y such that y has to take a binary value (i.e. 0 and 1)
Cost = 1000 * * y + 2400 * * (1-y)
>= 16 - M * y
Where M is a very large number (around 100000)
So, if is more than 16, y will be 0 and hence M * y will be 0 and in the cost function 1000 * * y term will be zero, thereby leaving only 2400 * * (1-y) or 2400 * in the cost function.
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