Question

The Boeing aircraft can carry a maximum of 300 passengers. A profit of $1500 is made on each business class ticket and a profit of $800 is made on each economy class ticket. The airline reserves at least 25 seats for business class. However, at least 3 times as many passengers prefer to travel by economy class than by business class. Determine how many tickets of each type must be sold in order to maximize the profit for the airline. What is the maximum profit?

1. State the decision variables
2. Write the profit equation
3. Write ALL the constraints for the problem.
4. Enter all the data and formulas in Excel
5. Solve the linear programming problem using Excel Solver

Answer 1

decision variables = profit

B = no. of business tickets

E = no. of economy tickets

P = 1500*B + 800*E dollars

constraints :

no. of seats = 300

E + B = 300

25 seats reserved for business class

therefore,

E <= 300-25

E <= 275

atleast 3 times passenger in economy as in business

E >= 3B

and bot E and B are greater than or equal to 0

E >= 0

B >= 0

constraints :

E + B = 300

E <= 275

E >= 3B

E >= 0

B >= 0

solving :

x = E , y = B

therefore for max profit E= 225,B= 75

max profit = $292500

P.S. (please upvote if you find the answer satisfactory)