Chap 9 WE - Worked Examples for Chapter 9 Example for...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Worked Examples for Chapter 9 Example for Section 9.3 Sarah has just graduated from high school. As a graduation present, her parents have given her a car fund of $21,000 to help purchase and maintain a certain three-year-old used car for college. Since operating and maintenance costs go up rapidly as the car ages, Sarah's parents tell her that she will be welcome to trade in her car on another three-year- old car one or more times during the next three summers if she determines that this would minimize her total net cost. They also inform her that they will give her a new car in four years as a college graduation present, so she should definitely plan to trade in her car then. (These are pretty nice parents!) The table gives the relevant data for each time Sarah purchases a three-year-old car. For example, if she trades in her car after two years, the next car will be in ownership year 1 during her junior year, etc. Sarah's Data Each Time She Purchases a Three-Year Old Car Purchase Operating and Maintenance Costs for Ownership Year Trade-in Value at End of Ownership Year Price 1 2 3 4 1 2 3 4 $12,000 $2,000 $3,000 $4,500 $6,500 $8,500 $6,500 $4,500 $3,000 When should Sarah trade in her car (if at all) during the next three summers to minimize her total net cost of purchasing, operating, and maintaining the cars over her four years of college? (a) Formulate this problem as a shortest-path problem. The following figure shows the network formulation of this problem as a shortest path problem. Nodes 1, 2, 3, and 4 are the end of Sarah's year 1, 2, 3, and 4 of college, respectively. Node 0 is now, before starting college. Each arc from one node to a second node corresponds to the activity of purchasing a car at the time indicated by the first of these two nodes and then trading it in at the time indicated by the second node. Sarah begins by purchasing a car now, and she ends by trading in a car at the end of year 4, so node 0 is the origin and node 4 is the destination .
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
The number of arcs on the path chosen from the origin to the destination indicates how many times Sarah will purchase and trade in a car. For example, consider the path This corresponds to purchasing a car now, then trading it in at the end of year 1 to purchase a second car, then trading in the second car at the end of year 3 to purchase a third car, and then trading in this third car at the end of year 4. Since Sarah wants to minimize her total net cost from now (node 0) to the end of year 4 (node 4), each arc length needs to measure the net cost of that arc's cycle of purchasing, maintaining, and trading in a car. Therefore, Arc length = purchase price + operating and maintenance costs - trade-in value. For example, consider the arc from node 1 to node 3. This arc corresponds to purchasing a car at the end of year 1, operating and maintaining it during ownership years 1 and 2, and then trading it in at the end of ownership year 2. Consequently, Length of arc from   1 3 to = 12,000 + 2,000 + 3,000 - 6,500 = 10,500 (in dollars).
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern