References
- There is also a very closely related literature on opportunity costing, some of which is concerned with the interpretation and application of the linear programming duals in the product mix problem. See Barron, M. J., ‘The application of linear programming dual prices in management accounting—some cautionary observations’, Journal of Business Finance, Vol. 4, I, Spring 1972, pp. 51–69 and Samuels, J. M., ‘Opportunity Costing: an application of mathematical programming’, Journal of Accounting Research, Vol. I, 2, Autumn 1963, pp. 182–191.
- While the discussion has been kept reasonably nontechnical some elementary knowledge of linear programming is assumed. As far as possible the popular approach of Baumol, W. J., Economic Theory and Operations Analysis (3rd Edition), Prentice-Hall 1972, has been used.
- Samuels op. cit. appears to be one of the few in this category
- Most costing text books, e.g. Horngren, C. T. Cost Accounting: a managerial emphasis (3rd Edition), Prentice- Hall 1972, take this view.
- The ICWA Report, A Report on Marginal Costing, Institute of Cost and Works Accountants, Gee and Co. 1961, is perhaps the most disturbing example
- The basic theorem of linear programming, Hadley, G., Linear Programming, Addison-Wesley 1962, pp. 80–84.
- See Hadley, op. cit., pp. 95–99.
- Note that the coefficient of s will automatically be negative since cr/ar > o.
- See Hadley, op. cit., 93–95.
- It is assumed throughout for ease of exposition that ci/aj cj/aj i ≠ j. The relaxation of this assumption allows alternative optimal solutions to exist but otherwise makes no material difference to the analysis.
- See Hadley, op. cit., pp. 387–395 or Gass, S. I., Linear Programming (3rd Edition), McGraw-Hill 1969, pp. 196–201.
- It is of course possible that the first activity exhausts the capacity in which case U will be empty.
- Interested readers may easily confirm that the same rules apply to the rare case of aj= o.
- See Hadlcy, op. at., p. 112.