In applying the principles of cost-benefit analysis to real world problems of resource allocation particular care must be taken to ensure that the welfare economic theory which underlies the cost-benefit technique is adhered to. Major problems arise where costs and benefits are used interchangeably to represent the good and bad attributes of a programme. Furthermore, in the presence of mutually exclusive projects, focussing attention upon the net benefits (or cost-benefit ratios) of individual projects as opposed to the net benefits of the use of budgeted resources can lead to biased estimates of the shadow price of projects and, consequently, errors in analysts' conclusions. As a result, economic appraisals of individual projects are not directly relevant for choosing between mutually exclusive projects of different sizes. Both types of problem are illustrated by reference to both simple examples and published economic appraisals of health care techniques. Integer programming is proposed and demonstrated as a method of selecting between mutually exclusive projects.