Equation used to minimize the distance function. Delta of w and d equals summing over all k (persons), the ratio of d sub k and cap A sub k times sum of two quantities. The first quantity is calculated as the product of the difference of a sub k and l sub k, and the natural logarithm of the ratio of the difference of a sub k and l sub k to the difference between c sub k and l sub k. The second quantity is defined as the product of the difference of u sub k and a sub k, and the natural logarithm of the ratio of the difference of u sub k and a sub k to the difference between u sub k and c sub k.