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Summary: A method for finding approximate solutions for continuous linear programming problems is suggested. The required conditions to be met are: a) the matrix associated with the integrals in the constraints is constant; b) all functions involved are of bounded variation; c) the matrices involved satisfy certain boundedness conditions, and d) there exist feasible solutions. The approximations converge almost everywhere to an optimal solution. The optimal solution is shown to be a function of bounded variation. The method is illustrated by means of a numerical example. Here, the approximate solution reveals also the structure of the exact (analytical) solution and makes its construction possible.

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