Answer to Question #98127 in Operations Research for Ahmad Rajpoot

Question

Suppose PIA is offering a new route: from Lahore to New York. The aircraft on this flight has a total of 280 seats. These seats can be converted into two categories: Business Class or Economy class, before flight schedule, depending on passengers buying any particular class of ticket. For the Lahore-New York flight to be profitable, PIA must sell a minimum of 80 Business class tickets and a minimum of 100 Economy class tickets. However, PIA does not want to have more than 150 seats in economy class to promote business class travelling. The airline earns a profit of $150 for each Business Class ticket and $100 for each Economy class ticket. How many of each category of ticket should be sold in order to MAXIMIZE total profit from of a flight. Use linear programming in following steps:

3. Using linear modelling method that you have learnt in the class, find out the solution.
4. Countercheck the answer with coordinates on the graph as well.
5. Find out the MINIMUM TOTAL PROFIT as well.

Answer 1

Let the number of seats in business class is x.

Let the number of seats in economy class is y.

$x+y<=280$

$x>=80$

$y>=100$

$y<=150$

$Profit = 150x + 100y$

According to graph,the function is bounded.Thus,it has a maximum and a minimum at its corner points.

The corner points from graph is (80,150),(130,150),(180,100),(80,100).

Co-ordinates Profit

(80,150) 27000

(130,150) 34500

(180,100) 37000

(80,100) 22000

MAX PROFIT --- 37000 at (180,100)- (Answer)

MIN PROFIT ----22000 at (80,100)