Communications on Pure and Applied MathematicsVolume 14, Issue 3 p. 355-369 Article Extreme varieties, concave functions, and the fixed charge problem Warren M. Hirsch, Warren M. HirschSearch for more papers by this authorAlan J. Hoffman, Alan J. HoffmanSearch for more papers by this author Warren M. Hirsch, Warren M. HirschSearch for more papers by this authorAlan J. Hoffman, Alan J. HoffmanSearch for more papers by this author First published: August 1961 https://doi.org/10.1002/cpa.3160140313Citations: 22AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Citing Literature Volume14, Issue3August 1961Pages 355-369 RelatedInformation