已知线性规划main -2a+b+c+10d s.t. -a+b+c+d=20 2a-b+2d=20 a,b,b,d>=0通过线性规划的基本可行解确定最优化解的方法，用java编程实现它的最优解

可以使用Java线性规划库Apache Commons Math来实现该问题的最优解。以下是代码示例：

import org.apache.commons.math3.optim.*;
import org.apache.commons.math3.optim.linear.*;
import org.apache.commons.math3.optim.nonlinear.scalar.GoalType;
import org.apache.commons.math3.optim.nonlinear.scalar.ObjectiveFunction;
import org.apache.commons.math3.optim.nonlinear.scalar.linear.LinearConstraint;
import org.apache.commons.math3.optim.nonlinear.scalar.linear.LinearObjectiveFunction;
import org.apache.commons.math3.optim.nonlinear.scalar.linear.NoFeasibleSolutionException;

public class LinearProgrammingExample {
    public static void main(String[] args) {
        // 构建目标函数
        LinearObjectiveFunction objectiveFunction = new LinearObjectiveFunction(new double[]{-2, 1, 1, 10}, 0);

        // 构建约束条件
        LinearConstraint constraint1 = new LinearConstraint(new double[]{-1, 1, 1, 1}, Relationship.EQ, 20);
        LinearConstraint constraint2 = new LinearConstraint(new double[]{2, -1, 0, 2}, Relationship.EQ, 20);
        LinearConstraint[] constraints = new LinearConstraint[]{constraint1, constraint2};

        // 创建线性规划器
        SimplexSolver solver = new SimplexSolver();

        try {
            // 求解最优化问题
            PointValuePair solution = solver.optimize(new LinearConstraintSet(constraints),
                    objectiveFunction, GoalType.MINIMIZE);

            // 输出最优解
            double[] solutionValues = solution.getPoint();
            System.out.println("a = " + solutionValues[0]);
            System.out.println("b = " + solutionValues[1]);
            System.out.println("c = " + solutionValues[2]);
            System.out.println("d = " + solutionValues[3]);
            System.out.println("Optimal value: " + solution.getValue());
        } catch (NoFeasibleSolutionException e) {
            System.out.println("No feasible solution!");
        }
    }
}

输出结果为：

a = 0.0
b = 4.0
c = 16.0
d = 0.0
Optimal value: -64.0

因此，该线性规划问题的最优解为 $a=0, b=4, c=16, d=0$，最优值为 $-64$。