Question

In USA, Airlines A and Airlines B have created some advantages for their loyal customers, especially for the NewYork to Miami flight. Airlines A provides 900 flight miles for each flight to its customers flying from NewYork to Miami. However, it gives 1000 (flight miles) extra points to more than 3 flights and  1350 (flight miles) to more than 6 flights within three months. While Airlines B gives 1200 points (flight miles) for each flight, it gives  1500 (flight miles) extra points for every 5 flights within three months. While the ticket price of Airlines A in NewYork- Miami is 800 dolar , the ticket price of Airline B is 600 dolar.

For a person who wants to make an NewYork to Miami flight 60 times in the next twelve months, please create an integer programming model to maximize flight miles.

Answer 1

Liner programming is attempt maximum and minimum solution to a problem function given certain constraints . That is the essence of linear programming .

Whereas Integer programming is a subset of linear programming , it has all characteristics of linear programming except that the solution to the problem must be in integer form and not in decimal form , a whole number .

Let X be the number of flights a person is taking from New York to Miami through Airline A and Y be the number of flights that person is taking from New York to Miami through Airline B .

Then we have following equations

X ≤ 60 .................(1)

Y ≤ 60 ................. (2)

X ≥ 0 ..................(3)

Y ≥ 0 ...... ..............(4)

Price for airline A per flight is 800 $ and for Airline B is 600 $

Minimize : Price of flights taken .

800X + 600Y .........(5)

Flight miles points per flight from New York to Miami through Airline A is 900 and for Airline B the flight miles points per flight from New York to Miami is 1200

So we have

Maximize : Flight miles ( points )

900X + 1200Y ..............(6)

The extra points will add up depending upon integer value of X and Y .