优化:种植小麦和水稻

Question

这是问题陈述

一位印度农民拥有一片农田，比如L平方公里长，他想种小麦或水稻，或者两者兼施。农民有有限数量的F公斤化肥和P公斤杀虫剂。

每平方公里的小麦都需要F1公斤化肥和P1公斤杀虫剂。每一平方公里的水稻种植都需要F2公斤化肥和P2公斤杀虫剂。设S1是出售一平方公里收获的小麦所获得的价格，S2是出售一平方公里收获的大米所获得的价格。

你必须通过选择种植小麦和/或水稻的地区，找到农民可以获得的最大总利润。

例如：

L= 10 Km2，F= 10 Kg，P=5 Kg，F1 =2 Kg，P1 =2 Kg，F2 =3 Kg，P2 =1 Kg，S1 = 14，S2 = 25。

在这种情况下，农民将获得最大的利润，如果他只播种水稻在3.33 Km2地区，最高利润价值将是83.33。

输入格式

唯一的输入将由9个整数分隔，L, F, P, F1, P1, F2, P2, S1, S2。

约束

1 <= L <= 10^4
1 <= F <= 10^4
1 <= P <= 10^4
F1 + F2< = F
P1 + P2 <= P
1 <= S1 <= 10^4
1 <= S2 <= 10^4

输出格式

输出将

• 最大利润修正在Km2中的
• 值高达2位，在应该种植小麦的地方校正到2位，在Km2中的
• 值修正到2位，应该种植水稻的位置校正到-2位数。

对于问题中考虑的示例，输出将是83.33 0.00 3.33。

样本测试用例

输入

10 10 5 2 2 3 1 14 25

输出

83.33 0.00 3.33

解释

假设L= 10 Km2，F= 10 Kg，P=5 Kg，F1 =2 Kg，P1 =2 Kg，F2 =3 Kg，P2 =1 Kg，S1 = 14，S2 = 25。农民在3.33 km2面积上种植水稻，不种植小麦，总利润最高，最大利润为83.33。

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我需要解决这个问题。然而，无法理解这句话本身。请帮帮我。

Answer 1

import java.text.DecimalFormat;
import java.util.Scanner;

public class Test {

    public static void main(String args[]) {
        // String input = "10,10,5,2,2,3,1,14,25";
        System.out.println(get_total_profit());
    }

    public static String get_total_profit() {
        // String[] inputs = input1.split(",");
        // Piece of farm land in square kilometer
        Scanner in = new Scanner(System.in);
        float L = in.nextInt(); // Float.valueOf(inputs[0]);
        // Fertilizer in kg
        float F = in.nextInt();// Float.valueOf(inputs[1]);
        // Insecticide in kg
        float P = in.nextInt();// Float.valueOf(inputs[2]);
        // Fertilizer required in kg for square kilometer of Wheat
        float F1 = in.nextInt();// Float.valueOf(inputs[3]);
        // Insecticide required in kg for square kilometer of Wheat
        float P1 = in.nextInt();// Float.valueOf(inputs[4]);
        // Fertilizer required in kg for square kilometer of Rice
        float F2 = in.nextInt();// Float.valueOf(inputs[5]);
        // Insecticide required in kg for square kilometer of Rice
        float P2 = in.nextInt();// Float.valueOf(inputs[6]);
        // Selling price of wheat per square kilometer
        float S1 = in.nextInt();// Float.valueOf(inputs[7]);
        // Selling price of rice per square kilometer
        float S2 = in.nextInt();// Float.valueOf(inputs[8]);

        // Result Variables
        float totalRiceInsecUsed = 0f;
        float totalRiceFertUsed = 0f;
        float totalWheatInsecUsed = 0f;
        float totalWheatFertUsed = 0f;
        float areaOfWheat = 0.00f;
        float areaOfRice = 0.00f;
        float amount = 0.00f;

        while (true) {
            if ((L == areaOfRice + areaOfWheat) || P == totalRiceInsecUsed + totalWheatInsecUsed
                    || F == totalRiceFertUsed + totalWheatFertUsed || F2 == 0 || F1 == 0 || P2 == 0 || P1 == 0) {
                break;
            }

            float calRiceProfit = Math.min(F / F2, P / P2) * S2;
            float calWheatProfit = Math.min(F / F1, P / P1) * S1;

            if (calRiceProfit > calWheatProfit) {
                float areaInsecUsed = P / P2;
                float areaFertUsed = F / F2;
                if (areaInsecUsed > areaFertUsed) {
                    L = L - areaFertUsed;
                    F2 = 0;
                    totalRiceFertUsed = totalRiceFertUsed + F2;
                    areaOfRice = areaOfRice + areaFertUsed;
                    amount = amount + areaFertUsed * S2;
                } else if (areaInsecUsed < areaFertUsed) {
                    L = L - areaInsecUsed;
                    P2 = 0;
                    totalRiceInsecUsed = totalRiceInsecUsed + areaInsecUsed;
                    areaOfRice = areaOfRice + areaInsecUsed;
                    amount = amount + areaInsecUsed * S2;
                }
            } else {
                float areaInsecUsed = P / P1;
                float areaFertUsed = F / F1;
                if (areaInsecUsed > areaFertUsed) {
                    L = L - areaFertUsed;
                    F1 = 0;
                    totalWheatFertUsed = totalWheatFertUsed + F1;
                    areaOfWheat = areaOfWheat + areaFertUsed;
                    amount = amount + areaFertUsed * S1;
                } else if (areaInsecUsed < areaFertUsed) {
                    L = L - areaInsecUsed;
                    P1 = 0;
                    totalWheatInsecUsed = totalWheatInsecUsed + areaInsecUsed;
                    areaOfWheat = areaOfWheat + areaInsecUsed;
                    amount = amount + areaInsecUsed * S1;
                }
            }

        }
        DecimalFormat df = new DecimalFormat();
        df.setMaximumFractionDigits(2);
        df.setMinimumFractionDigits(2);
        return df.format(amount) + "," + df.format(areaOfWheat) + "," + df.format(areaOfRice);
    }

}

Answer 2

这是一个线性优化问题(https://en.wikipedia.org/wiki/Linear_programming)，通常用单纯形算法(https://en.wikipedia.org/wiki/Simplex_algorithm)求解。

Answer 3

import java.text.DecimalFormat;
import java.util.Scanner;

public class CandidateCode {

    public static void main(String args[]) {
        // String input = "10,10,5,2,2,3,1,14,25";
        System.out.print(get_total_profit());
    }

    public static String get_total_profit() {
        // String[] inputs = input1.split(",");
        // Piece of farm land in square kilometer
        Scanner in = new Scanner(System.in);
        float L = in.nextInt(); // Float.valueOf(inputs[0]);
        // Fertilizer in kg
        float F = in.nextInt();// Float.valueOf(inputs[1]);
        // Insecticide in kg
        float P = in.nextInt();// Float.valueOf(inputs[2]);
        // Fertilizer required in kg for square kilometer of Wheat
        float F1 = in.nextInt();// Float.valueOf(inputs[3]);
        // Insecticide required in kg for square kilometer of Wheat
        float P1 = in.nextInt();// Float.valueOf(inputs[4]);
        // Fertilizer required in kg for square kilometer of Rice
        float F2 = in.nextInt();// Float.valueOf(inputs[5]);
        // Insecticide required in kg for square kilometer of Rice
        float P2 = in.nextInt();// Float.valueOf(inputs[6]);
        // Selling price of wheat per square kilometer
        float S1 = in.nextInt();// Float.valueOf(inputs[7]);
        // Selling price of rice per square kilometer
        float S2 = in.nextInt();// Float.valueOf(inputs[8]);

        // Result Variables
        float totalRiceInsecUsed = 0f;
        float totalRiceFertUsed = 0f;
        float totalWheatInsecUsed = 0f;
        float totalWheatFertUsed = 0f;
        float areaOfWheat = 0.00f;
        float areaOfRice = 0.00f;
        float amount = 0.00f;

        while (true) {
            if ((L == areaOfRice + areaOfWheat) || P == totalRiceInsecUsed + totalWheatInsecUsed
                    || F == totalRiceFertUsed + totalWheatFertUsed || F2 == 0 || F1 == 0 || P2 == 0 || P1 == 0) {
                break;
            }

            float calRiceProfit = Math.min(F / F2, P / P2) * S2;
            float calWheatProfit = Math.min(F / F1, P / P1) * S1;

            if (calRiceProfit > calWheatProfit) {
                float areaInsecUsed = P / P2;
                float areaFertUsed = F / F2;
                if (areaInsecUsed > areaFertUsed) {
                    L = L - areaFertUsed;
                    F2 = 0;
                    totalRiceFertUsed = totalRiceFertUsed + F2;
                    areaOfRice = areaOfRice + areaFertUsed;
                    amount = amount + areaFertUsed * S2;
                } else if (areaInsecUsed < areaFertUsed) {
                    L = L - areaInsecUsed;
                    P2 = 0;
                    totalRiceInsecUsed = totalRiceInsecUsed + areaInsecUsed;
                    areaOfRice = areaOfRice + areaInsecUsed;
                    amount = amount + areaInsecUsed * S2;
                }
            } else {
                float areaInsecUsed = P / P1;
                float areaFertUsed = F / F1;
                if (areaInsecUsed > areaFertUsed) {
                    L = L - areaFertUsed;
                    F1 = 0;
                    totalWheatFertUsed = totalWheatFertUsed + F1;
                    areaOfWheat = areaOfWheat + areaFertUsed;
                    amount = amount + areaFertUsed * S1;
                } else if (areaInsecUsed < areaFertUsed) {
                    L = L - areaInsecUsed;
                    P1 = 0;
                    totalWheatInsecUsed = totalWheatInsecUsed + areaInsecUsed;
                    areaOfWheat = areaOfWheat + areaInsecUsed;
                    amount = amount + areaInsecUsed * S1;
                }
            }

        }
        DecimalFormat df = new DecimalFormat();
        df.setMaximumFractionDigits(2);
        df.setMinimumFractionDigits(2);
        return df.format(amount) + " " + df.format(areaOfWheat) + " " + df.format(areaOfRice);
    }

}