A package express carrier is considering expanding the
fleet of aircraft used to transport packages. Of primary importance is that
there is a total of $350 million allocated for purchases. Two types of aircraft
may be purchased – the C1A and the C1B. The C1A costs $25 million, while the
C1B costs $18 million. The C1A can carry 60,000 pounds of packages, while the
C1B can only carry 40,000 pounds of packages. Of secondary importance is that
the company needs at least 10 new aircraft. It takes 150 hours per month to
maintain the C1A, and 100 hours to maintain the C1B. The least level of
importance is that there are a total of 1,200 hours of maintenance time
available per month.
Part 1: Formulate this as an integer programming problem
to maximize the number of pounds that may be carried.
Part 2: Rework the problem differently than in Part 1 to
suppose the company decides that what is most important to them is that they
keep the ratio of C1Bs to C1As in their fleet as close to 1.2 as possible to
allow for flexibility in serving their routes. Formulate the goal programming
representation of this problem, with the other three goals having priorities P2,
P3, and P4, respectively.
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