This post may be a little lengthy, so please bare with me if you can help. The problem is: A cruise liner has 4 classes of accommodations. Following are the # of reservations made, # of reservations available, and cost per room for each class:
Super Deluxe, 100, 160, \$3000
First Class, 145, 150, \$2600
Tourist, 170, 180, \$2000
Economy, 265, 230, \$1800
The company has a policy that if a customer is holding a certain type reservation that cant be filled, then the customer will be bumped up to the next class at no additional cost.
I need to determine the number of accommodations in each class to be received by customers that will MINIMIZE THE LOSS OF POTENTIAL REVENUE.
My observations: To minimize foregone revenue due to bumped passengers, a passenger will only be bumped up one class. If the class they are to be bumped to is full, a passenger from the more expensive class will be bumped up to make room for them. Therefore, if we let Xi=the # passengers bumped into class i, I think the objective function should be "Min Z=\$400Xs(super deluxe)+ \$600Xf(first class)+ \$200Xt(tourist)+ \$0Xe(economy)". The only constraints I see are regarding the total # reservations for each class, so I came up with: (all < or > are intended as less/greater than or equal to)

Min Z=\$400Xs + \$600Xf + \$200Xt + \$0Xe
s.t. Xs<160, Xf<150, Xt<180, Xe=0, Xs,f,t,e>0

Does this model look right, or am I way off? I came up with these constraints by figuring that the maximum amount of money you could possibly lose in each category would be in the event that the more expensive class had 0 reservations and you completely filled it with bumps from the next lower class. Remember, I am trying to MINIMIZE FOREGONE REVENUE, not necessarily to maximize profit. I have to enter the data into the Management Scientist software we are using and print out the solution it gives. I am not worried about the actual # of reservations given in the problem, as the model needs to work for any given # of reservations. I will fill in the actual amounts later. If anyone can give me some feedback as to whether I am on the right track or not, I would really appreciate it. I only have a few days to complete this, so any ideas you can offer will help greatly. Thanks for your time.

The objective function looks right, the constraints are not right. First, you want the constraints at <= You say tha Xs is the number bumped to super deluxe. Let S be the original number in superdeluxe. So the constraint is S+Xs <= 160. Let F be the original number in first class. The constraint here is F-Xs+Xf<=150. And so on.

Ah. I had thought about F+Xf<=150 and T+Xt<=180 before but forgot to subtract out the people bumped out of it. Thanks for the help!

1. 👍 0
2. 👎 0
3. 👁 87

## Similar Questions

1. ### Math

is this the correct answer? I might post more on this exact post, so please bare with me? These are proportions 1.) 2:5 = 4:y Answer: y=2

asked by Bryce on September 6, 2011
2. ### To Sha -- Child Development

asked by Ms. Sue on February 27, 2009
3. ### To: Kathy -- finance

I removed your two posts containing a lengthy assignment that appears to be a semester project. If you're posting to be sure it's included in Jiskha archives, you're misusing this forum. If you honestly want some help, please post

asked by Ms. Sue on December 19, 2010
4. ### Math

The perimeter of the rectangle is 54 meters the lengthy of the rectangle is five less than three times with what is the lengthy of the rectangle

asked by Genevive on November 21, 2016
5. ### English Linguistics

Hey :) I have a quizz on Friday, and on the shetts, it seems to be a mistake... First it stands there: Complements can be expresseed by adjectives or a bare noun. Objects can't. And then at an example sentences cannot be replaced

asked by Minnie on February 12, 2013
6. ### Physics

A 850 kg car skidding on an icy highway at 32.5 km/h slides onto some bare pavement. If the coefficient of friction between the tires and the bare pavement is 0.200, what time(s) does it take for the car to stop? HOW do i get the

asked by Brina on August 2, 2011
7. ### English, poetry, end rhyme

From “The Chimney-Sweeper” by William Blake When my mother died I was very young, And my father sold me while yet my tongue Could scarcely cry “Weep! weep! weep! weep!” 4 So your chimneys I sweep, and in soot I sleep .

asked by BeautifulGamer333 on March 12, 2018
8. ### statistics

1.What’s the most appropriate procedure for evaluating the relationship between tenure and divorce? 2.What is the correlation and how can it be interpreted in terms of magnitude, direction and practical importance? 3.How much of

asked by tina on August 25, 2013
9. ### To Amanda

I deleted same lengthy assignment that you've posted three times in the last hour or so. "Posted by Amanda on Thursday, November 11, 2010 at 5:40pm. Continuing Cookie Chronicle (Note: This is a continuation of the Cookie Chronicle

asked by Ms. Sue on November 11, 2010
10. ### Math

A farmer builds a straight fence that's 49 ft. He puts a post every 7ft. How many post does he need. A post is at the beginning and end How can you show the relationships in the problem Solve and explain your reasoning 8 post. I

asked by Anonymous on May 23, 2016