Question

An airline owns an aging fleet of Boeing 737 Jet airplanes. It is considering a major purchase of up to 17 new boeing 787 and 767 jets. The decision must take into account the following: 1) Finance up to $1.6 Billion in purchases; 2) each 787 costs $80 Million and each 767 costs $110 Million; 3) at least 1/3 of the planes purchased should be the 787; 4) annual maintenance budget is no more than $8 Million; 5) Annual maintenance per 787 is $800,000 and $500,000 for each 767; 6) each 787 can carry 125,000 passengers annually, each 767 can carry 81,000 passengers annually. Formulate this as an integer programming problem to maximize passenger carrying abilities

Answer 1

An integer programming problem is formulated to maximize passenger carrying abilities considering various constraints and objectives related to the purchase of Boeing 787 and 767 jets by an airline.

Step-by-step explanation:

To formulate this as an integer programming problem, we need to define the decision variables, objective function, and constraints. Let's denote the number of 787 jets purchased as x and the number of 767 jets purchased as y.

The objective is to maximize the passenger carrying abilities, which can be represented by the following objective function: Maximize 125,000x + 81,000y.

The constraints include:

• Finance constraint: 80,000,000x + 110,000,000y ≤ 1,600,000,000
• At least 1/3 of the jets should be 787: x ≥ (1/3)(x + y)
• Annual maintenance budget constraint: 800,000x + 500,000y ≤ 8,000,000
• Non-negativity constraint: x, y ≥ 0