Linear programming (LP): The linear programming(LP) is also known as linear optimization. Consider a mathematical model, and its requirements are used to represent by the linear relationships. The linear programming is the best method to achieve the best outcome of this mathematical model. The outcomes may be, maximum profit or lower cost. The linear optimization is also called as mathematical optimization because, it is a special case of mathematical programming. More formally, the LP is a technique for optimizing linear objective function subject to constraints of linear equality and linear inequality.

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7. See the code below and solve the following. public class Test { public static void main(String[] args) { int result = 0; } result = fn(2,3); System.out.println("The result is: + result); // fn(x, 1) = x // fn(x, y) = fn(x, y-1) + 2, when y>1 public static int fn(int x, int y) { if (x <= 1) return x; else return fn(x, y-1) + 2; } } 7-1. This program has a bug that leads to infinite recursion. Modify fn(int x, int y) method to fix the problem. (2 point) 7-2. Manually trace the recursive call, fn(2,3) and show the output (step by step). (2 point) 7-3. Can you identify the Base Case in recursive method fn(int x, int y)? (1 point)

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Chapter 3, Problem 4RP

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Linear programming (LP):

The linear programming(LP) is also known as linear optimization.

Consider a mathematical model, and its requirements are used to represent by the linear relationships. The linear programming is the best method to achieve the best outcome of this mathematical model. The outcomes may be, maximum profit or lower cost.

The linear optimization is also called as mathematical optimization because, it is a special case of mathematical programming.

More formally, the LP is a technique for optimizing linear objective function subject to constraints of linear equality and linear inequality.

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