An airline owns an aging fleet of Boeing 737 jet airplanes.

It is considering a major purchase of up to 17 new Boeing model 757 and 767 jets. The decision must take into account numerous cost and capability factors, including the following:

(1) The airline can finance up to $1.6 billion in purchases;

(2) Each Boeing 757 will cost $80 million, and each Boeing 767 will cost $110 million;

(3) At least one-third of the planes purchased should be the longer-range 757;

(4) The annual maintenance budget is to be no more than $8 million;

(5) The annual maintenance cost per 757 is estimated to be $800,000, and it is $500,000 for each 767 purchased;

(6) Each 757 can carry 125,000 passengers per year, whereas each 767 can fly 81,000 passengers annually. Formulate this as an integer programming problem to maximize the annual passenger-carrying capability. What category of integer programming problem is this? Solve this problem.