The use of linear programming in decision making has been widespread for twenty to thirty years, with its theoretical and solution concepts well documented and explored. In spite of its wide use one main difficulty in linear programming remains, and that is the fact that linear programming problems are defined with only one objective function. A. Charnes and W. W. Cooper, through continuing research, developed the concept of goal programming which enables one to solve linear programming problems with multiple objectives. This dissertation presents computational procedures which will enable one to solve a large-scale linear goal programming problem as well as its multidimensional dual problem. Applications in statistics and industry are explored.