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