Solving mathematical programming problems without the aid of electronic computers is very time consuming even for a mathematical model consisting of only a few constraints and variables. The objective of this report is to illustrate the use of mathematical programming computer routines available at Utah State University. Computer routines discussed are the International Business Machines (IBM), Mathematical Programming System (MPS) package, a quadratic programming routing, a zero-one integer programming routing, and a transportation code. The MPS package is a product of IBM; the quadratic programming routing was develop by the author: the last three routines were obtained from the IBM share library. Source decks, 80-80 lists, and execution lists are available at the Department of Applied Statistics and Computer Science, the Department of Economics, and the Utah State Computer Center of Utah State University (USU) for all the computer programs indicated above excluding the MPS package. Each source deck, complete with job control language and sample problem input is read to run on the computer with the addition of a valid job card. The 80-80 list for each program is an exact duplicate of its corresponding deck. The execution list shows the output that is to result upon the execution of a given program and sample input deck. Within this report a discussing is prepared for each sample problem. First the problem is defined and the mathematical model for solution of the problem is developed. Second, explanation is provided on how the input cards are prepared, and finally an interpretation of the program output is included. The MPS package is stored on disk at the U.S.U. Computer Center. Sample problems are provided in this report which illustrate how to use the MPS package. Also included in the report are references to where other sample problems may be found which illustrate the use of the MPS package. Even though the Job Control Language (JCL) cards included in the illustrations vary with computer installation and with time, these are included so that the user will have an idea of the JCL needed to run the programs. Various words within this report require a blank character. Since a blank character within a word would be confusing, the symbol "Δ" is used in place of the blank character.