Maximum product What two nonnegative real numbers with a sum of 23 have the largest possible product?

Solution Step 1: Consider two nonnegative real numbers x and y Sum of x and y is constraints which is 23 that is x+y=23 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 x+y=23 y = 23 x Step 3: Substituting for y the objective function becomes P=xy P=x(23-x) 2 P = 23x x ; 0 x 23 Which is the function of single variable x with P(0)=P(23)=0