A Modified Simplex Solution for Linear Programming with Variable Capital Restrictions

INEAR programming is becoming a widespread and useful tool in economic guidance. However, possibilities still exist for increasing the flexibility in application of the method to a wider range of situations, and in lessening time or cost of computations. This paper reports a method whereby linear program solutions can be provided easily for a large number of capital situations. The results can be presented in a simple manner for use by extension personnel, or by farmers themselves. Most farmers have limited amounts of capital at their command. Hence, the capital restriction used for one programming situation does not apply to another farm with more or less capital available. In many farming regions, a large number of farms have similar soil, acreage, building and family labor restrictions, whereas capital is highly variable. Many previous programming studies have attempted to meet this problem by computing programs for a few discrete capital levels, such as $5,000, $10,000, etc. However, the method proposed here allows capital to be a continuous variable and hence can replace a number of discrete solutions. It derives the optimum production plan continuously for each and every level of capital; not merely for discrete, arbitrary levels.