To solve this problem, let's define the variables and set up the equations based on the given data.

Variables:

1. Let $x$ represent the number of Airbus A330-300s.
2. Let $y$ represent the number of Boeing 767-300ERs.
3. Let $z$ represent the number of Boeing Dreamliner 787-9s.

Information given:

1. Seating capacity and cost per aircraft:

   • Airbus A330-300 seats 330 passengers and costs $260 million.
   • Boeing 767-300ER seats 270 passengers and costs $220 million.
   • Boeing Dreamliner 787-9 seats 240 passengers and costs $290 million.

2. Constraints:

   • Total seating capacity required: 5,820 passengers.
   • Total spending goal: $5,530 million.
   • The company has a policy of buying twice as many Boeings as Airbuses, meaning $y + z = 2x$.

Equations:

1. Passenger capacity equation: $330x + 270y + 240z = 5820$

2. Cost equation: $260x + 220y + 290z = 5530$

3. Boeing-to-Airbus ratio (policy) equation: $y + z = 2x$

With these equations, we can solve for $x$, $y$, and $z$ to find the required number of each aircraft type.

I'll proceed with solving this system of equations.from sympy import symbols, Eq, solve

Define variables

x, y, z = symbols('x y z')

Define equations based on the problem statement

eq1 = Eq(330x + 270y + 240z, 5820) # Passenger capacity equation eq2 = Eq(260x + 220y + 290z, 5530) # Cost equation eq3 = Eq(y + z, 2*x) # Boeing-to-Airbus ratio equation

Solve the system of equations

solution = solve((eq1, eq2, eq3), (x, y, z)) solution{x: 7, y: 5, z: 9}{x: 7, y: 5, z: 9}successThe solution to the problem is:

• Airbus A330-300s: 7 units
• Boeing 767-300ERs: 5 units
• Boeing Dreamliner 787-9s: 9 units

This configuration meets both the seating and budget requirements while following the policy of purchasing twice as many Boeing aircraft as Airbuses.

Would you like a breakdown of the calculations or further explanation on any part?

Related Questions:

1. How would the solution change if the seating capacity requirement increased by 10%?
2. What if the budget was decreased by $500 million—how would that affect the quantities?
3. If a new type of aircraft was introduced with different specifications, how would that affect the calculations?
4. What other configurations could potentially meet the requirements if the policy constraint was relaxed?
5. How would fluctuations in aircraft prices impact the purchasing decision?

Tip:

When solving linear systems with multiple variables, organizing the information into equations based on constraints simplifies finding a solution systematically.