Maximum length What two nonnegative real numb ? ers? ? nd ? whose sum is 2 2 2 2 23 maximize ?a +b ? Minimize a +b ?
Solution Step 1: Given data Two nonnegative real numbers a and b Sum of a and b is constraints which is 23 that is a+b=23 2 2 Sum of square of a and b is objective function P=a +b Product of x and y is objective function P=xy Step 2 The first step is to use the constraints to express the objective function P in terms of single variable For this a+b=23 b = 23a Step 3: Substituting for b the objective function becomes P=a +b 2 P=a +(23a) ; 2 0 a 23 2 Which is the function of single variable x with P(0)=P(23)=(23) So P has maximum value at a=0 or a=23 And if P is in terms of b the P has maximum value at b=0 or b=23 We conclude that P has maximum value for two nonnegative real numbers 0 and 23