Their cruise would port out of New Orleans and promised seven days with a panopl
ID: 453375 • Letter: T
Question
Their cruise would port out of New Orleans and promised seven days with a panoply of excursions in Jamaica, Cozumel, and Grand Cayman. A list of excursions at each site and key features of each appear in the table. The excursions were all day affairs, so it was possible to engage in only one per port. The cruise ship sailed at night and docked at each of these three ports at the crack of dawn. By dinner time, the ship was on its way to the next port and next set of excursions. The couple was energetic and active for a pair of 52 year-olds., and while enjoying an upper middle class lifestyle, they didn't want to spend money on excursions that might be better spent on tacky souvenirs. The couple therefore budgeted $250 for the excursions — the prices shown are per couple, so for example, the $60 will pay for both of them to fill up on jerk chicken and mannish water.
For each of the duplicate excursions (e.g., snorkeling is offered in all three ports), the couple researched the quality of the activity and ranked the excursion among the available alternatives, with higher numbers indicating better quality. Thus, snorkeling in Jamaica is better than in Cozumel, and snorkeling in Cozumel is better than in Grand Cayman. For the unique experiences, i.e., the turtle farm, the default rating was the a 3.
Site
Rating
Activity
Cost
Jamaica
3
snorkeling
$100
Jamaica
1
party island
$95
Jamaica
2
horseback ride
$120
Jamaica
3
local cuisine
$60
Cozumel
2
snorkeling
$110
Cozumel
3
party island
$55
Cozumel
1
horseback ride
$70
Cozumel
2
local cuisine
$90
Cozumel
3
tequila tasting
$130
Grand Cayman
1
snorkeling
$90
Grand Cayman
2
party island
$60
Grand Cayman
3
horseback ride
$110
Grand Cayman
1
local cuisine
$130
Grand Cayman
3
turtle farm
$95
What is an appropriate objective function for this vacation?
What is an appropriate objective function and constraints for this vacation?
Part 2
The first day on the cruise was a "day at sea" meaning no port of call, and only the amenities onboard for amusement. Restless and uncomfortably full after seven trips through the buffet, the management scientist gambled away most of his vacation money at the onboard casino. The excursions would be a necessity, but now it became less important to maximize the joy of the excursions and more vital to get off the boat as cheaply as possible while still staying busy at the three pots of call. What is an appropriate objective function for this modified cruise vacation?
Site
Rating
Activity
Cost
Jamaica
3
snorkeling
$100
Jamaica
1
party island
$95
Jamaica
2
horseback ride
$120
Jamaica
3
local cuisine
$60
Cozumel
2
snorkeling
$110
Cozumel
3
party island
$55
Cozumel
1
horseback ride
$70
Cozumel
2
local cuisine
$90
Cozumel
3
tequila tasting
$130
Grand Cayman
1
snorkeling
$90
Grand Cayman
2
party island
$60
Grand Cayman
3
horseback ride
$110
Grand Cayman
1
local cuisine
$130
Grand Cayman
3
turtle farm
$95
Explanation / Answer
The objective function is to maximize the number of excursions. Let locations be denoted as j,c and g and the activites as 1-Snorkeling, 2-party island, 3-horseback rode, 4-local cuisine, 5-tequila tasting, 6-turtle farm. If x denotes the decision variable, then the objective function can be written
Max 3xj1 + xj2 + 2xj3 + 3xj4 + 2xc1 + 3xc2 + 1xc3 + 2xc4 + 3xc5 + 1xg1 + 2xg2 + 3xg3 + 1xg4 + 3xg6
Subject to constraints
100xj1 + 95xj2 + 120xj3 + 60xj4 + 110xc1 + 55xc2 + 70xc3 + 90xc4 + 130xc5 + 90xg1 + 60xg2 + 110xg3 + 130xg4 + 95xg6 <= 250
xj1 + xj2 + xj3 + xj4 = 1
xc1 + xc2 + xc3 + xc4 + xc5 =1
xg1 + xg2 + xg3 + xh4 + xg6 =1
where all variables can only be 0 or 1
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