A Boston-based middle manager recently received an exciting e-mail offer from American Airlines. Because of her long-time loyalty, she is eligible to obtain LIFETIME Platinum elite status on American if she fulfills a special “challenge”—flying 20,000 miles and 12 segments between October 1 and December 31. She covets the perks that come from Platinum status: priority check-in and boarding, lounge access, 100 percent bonus on miles flown. The challenge is definitely doable; she has friends and family to visit in Los Angeles (5,200 miles roundtrip), Miami (2,520 miles), and Durham, North Carolina (1,224 miles)—all of which have American direct flights from Boston. (Each roundtrip counts as two flight segments.)

a. She is ready to book her trips, and the cheapest American roundtrip fares to the three cities are $425, $300, and $200, respectively. How should she plan her numbers of trips to these destinations to meet the mile and segment challenge at minimum total cost? Using a spreadsheet and optimizer, formulate and solve her linear program.

(In the optimizer menu, be sure to include the constraint that the number of trips to each destination must be an integer.)

b. How would her trip plan and total cost change if 25,000 flown miles were required? What if only 10 segments (and 20,000 miles) were needed?