An aeroplane can carry a maximum of 200 passengers. A profit of Rs 1000 is made on each executive class ticket and a profit of Rs 600 is made on each economy class ticket. The airline reserves at least 20 seats for executive class. However, at least 4 times as many passengers prefer to travel by economy class than by the executive class. The maximum profit that can be made is equal to
An aeroplane can carry a maximum of 200 passengers. A profit of Rs 1000 is made on each executive class ticket and a profit of Rs 600 is made on each economy class ticket. The airline reserves at least 20 seats for executive class. However, at least 4 times as many passengers prefer to travel by economy class than by the executive class. The maximum profit that can be made is equal to
The correct option is A 136000
Let, the airline sells x tickets of executive class and y tickets of economy class. We want to find the maximum profit made by selling x executive class and y tickets of economy class. For executive class the profit made by selling one ticket is 1000 and for economy class it is 600.
So the total profit we get by selling x tickets of executive class and y tickets of economy class is 1000x+600y. We want to maximize this. This is our objective function.
z = 1000x + 600y
What are the constraints of this problem?
Since x and y are number of tickets, x ≥ 0 and y ≥ 0 ------(1)
Its given that the number of seats is 200.
=> x + y ≤ 200 ------(2)
The airline reserves at least 20 seats for executive class.
=> x ≥ 20 ------(3)
=> At least 4 times as many passengers prefer to travel by economy class than by the executive class.
=> y ≥ 4x or y - 4x ≥ 0 ------(4)
These are the four constraints of this problem.
Let us now draw the common region of these constraints. It would be the shaded region in the diagram.
We know by theorem 1 and 2 in linear programming, the maximum value of profit will occur at one of those corner points. We will substitute the values of x and y of each corner point in the objective function z = 1000x+600y and find out which is the highest.
The corner point (40, 160) gives the highest value equal to 136000. This is maximum profit we can make.
Let, the airline sells x tickets of executive class and y tickets of economy class. We want to find the maximum profit made by selling x executive class and y tickets of economy class. For executive class the profit made by selling one ticket is 1000 and for economy class it is 600.
So the total profit we get by selling x tickets of executive class and y tickets of economy class is 1000x+600y. We want to maximize this. This is our objective function.
z = 1000x + 600y
What are the constraints of this problem?
Since x and y are number of tickets, x ≥ 0 and y ≥ 0 ------(1)
Its given that the number of seats is 200.
=> x + y ≤ 200 ------(2)
The airline reserves at least 20 seats for executive class.
=> x ≥ 20 ------(3)
=> At least 4 times as many passengers prefer to travel by economy class than by the executive class.
=> y ≥ 4x or y - 4x ≥ 0 ------(4)
These are the four constraints of this problem.
Let us now draw the common region of these constraints. It would be the shaded region in the diagram. We know by theorem 1 and 2 in linear programming, the maximum value of profit will occur at one of those corner points. We will substitute the values of x and y of each corner point in the objective function z = 1000x+600y and find out which is the highest.
The corner point (40, 160) gives the highest value equal to 136000. This is maximum profit we can make.
