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; and (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