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# Maximize the total profit of all the persons X in Java

We are given 5 Integer variables Num, P1, P2, profit_P1, profit_P2 and the task is to maximize the profit and from all the natural numbers in the range of [1,Num]. The approach here is that if a positive number is divisible by P1 the profit increases by profit_P1 and similarly if if the number in the range is divisible by P2 the profit margin of profit_P2 increases. Also, the profit from a positive integer can be added at most once.

## Let us understand with example:-

**Input **− int num = 4, P1 = 6, P2 = 2, profit_P1 = 8, profit_P2 = 2;

**Output **− Maximize the total profit of all the persons X 4

**Explanation **−Here we have number ranged from 1 to 4([1,Num(4)])

No number in the series is divisible by P1

1 and 2 is divisible by P2

1 and 2 is divisible by P2 to get the profit of 2*2=**4**

**Input **− num = 3, P1 = 1, P2 = 2, profit_P1 = 3, profit_P2 = 4

**Output **− Maximize the total profit of all the persons X 10

**Explanation **− 1, 2 and 3 are divisible by A.

2 is the only number in the given range which is divisible by B.

2 is divisible by both A and B.

1 and 3 can be divided by A to get the profit of 2 * 3 = 6

2 can be divided by B to get the profit of 1 * 4 = 4

2 is divisible by both but in order to maximise the profit it is divided by B instead of A.

## Approach used in the below program is as follows −

We are been given with 6 integer variables that includes the positive number range(Num), P1 which depicts the first person, P2 depicts the second person,profit_P1 which resembles the profit of person 1(i.e. if the number in the given number range is divisible by P1 profit_P1 rises), and similarly profit_P2.

Inside the main function a method is called(profitMaximisation) which is the utility method for all the calculation.

Inside the function it can be seen that every number which is divisible with both P1 and P2 only if the number is a multiple of the LCM of either P1 or P2.Also it should be divided with the number that gives more profit.

So here it is calculated by

**profit_P1 * (num / P1) + profit_P2 * (num / P2) – min(profit_P1, profit_P2) * (num / lcm(P1, P2))**.A method is introduced CalculateGcd() to calculate the lcm of the given numbers.

The final output is captured in the main method and displayed to user as output.

## Example

public class testClass{ static int CalculateGcd(int n1, int n2){ if (n2 == 0) return n1; return CalculateGcd(n2, n1 % n2); } static int profitMaximisation(int n, int a, int b, int x, int y){ int result = x * (n / a); result += y * (n / b); result -= Math.min(x, y) * (n / ((a * b) / CalculateGcd(a, b))); return result; } public static void main(String[] args){ int num = 6, P1 = 6, P2 = 2, profit_P1 = 8, profit_P2 = 2; System.out.println("Maximize the total profit of all the persons X "+profitMaximisation(num, P1, P2, profit_P1, profit_P2)); } }

## Output

If we run the above code it will generate the following Output

Maximize the total profit of all the persons X 12