We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
Published online by Cambridge University Press: 06 July 2010
The Standard Linear Programming Problem
Let us begin this chapter with a pair of examples.
Example 7.1a The following investment opportunity is available from Monday to Friday of the forthcoming week. For any amount x, if you invest x on a day and 2x on the next day then you will receive 4x at the beginning of the third day. The amount received at the beginning of a day can then be used that day for starting a new investment or for continuing an ongoing investment. There are no payments received after Friday (so one should not begin a new investment on Thursday or Friday). If you invest x but cannot put down 2x on the next day then you lose the initial investment x. For instance, starting with a fortune of 1, it does not pay to invest more than 1/3 on day 1. For if x > 1/3 is invested on day 1 then your remaining capital of 1 − x will not be sufficient to enable you to invest 2x on day 2, resulting in a forfeit of the initial investment x. On the other hand, you could invest 1/3 on day 1 and 2/3 on day 2, which yields the return 4/3 at the beginning of day 3; you could then use that amount to begin a second investment by investing 4/9 (one third of 4/3) on day 3 and 8/9 on day 4, thus earning a return of 16/9 on day 5. Can you do better?
To save this book to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Find out more about the Kindle Personal Document Service.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.
