A five year linear programming farm planning model was constructed to include the use of sewage sludge as a primary crop nutrient source. The five year planning period permitted the inclusion of nitrogen decay rates reflecting the residual amounts of nitrogen from sludge and manure which are mineralized over time. Net farm incomes were maximized and compared for a medium sized dairy farm representative of those found in Pennsylvania. Twenty-two scenarios depicting various operating conditions were examined. Some of the variations included the purchase of sludge at different prices, the use of free nine percent nitrogen or 4.2 percent nitrogen sludge, spring and fall application of sludge and manure, the use of free sludge when heifer corral manure was sold, and sludge use under various nitrogen application restrictions. Variables of interest in the optimal programs were than compared and discussed.
Under the conditions assumed for the analyses, net revenues were higher when sludge was used than when it was not. However, only a small percentage difference between the highest and the lowest net revenues resulted over the five year period, given a variety of operating circumstances. The combination of nine percent nitrogen sludge, manure, and fertilizer yielded the highest net revenue when sludge was free and applied either annually in the spring or semiannually in the spring and fall. Further, when sludge was purchased at $10.00/dry ton and $20.00/dry ton for spring and fall application, the combination of nine percent nitrogen sludge and manure again resulted in the highest net revenue.
The nitrogen application restrictions were at their upper limits when sludge use was included in the optimal solution, but were not binding when sludge was not used. More sludge was applied when the nitrogen application restrictions were relaxed, resulting in higher net income. The reduced costs associated with the non-negativity constraint on sludge indicated that it would often be more costly to use more than the optimal amount of sludge, than less than the optimal amount, because less manure would be used and more fertilizer would have to be purchased to maintain nitrogen application limits and meet crop nutrient requirements.
The calculation of net present values for the two sludge contents considered provided value estimates which were in accord with the linear programming solutions. Although the programming results are situation-specific, the model's structure and coefficients may be modified to accommodate different farm activities and restrictions.