Find two positive numbers whose sum is 16 such that the product of one number and the cube of the other number is a maximum.
A) 4 and 12
B) 1 and 15
C) 3 and 13
D) 8 and 8
E) 9 and 7

Question

Quizplus · Accepted Answer

Let the two numbers be x and y. Then, x + y = 16 and xy^3 is to be maximized.Using AM-GM inequality, we have:(x + y)/2 >= sqrt(xy)=> 16/2 >= sqrt(xy)=> 8 >= sqrt(xy)=> 64 >= xy=> xy <= 64Therefore, the maximum value of xy^3 occurs when xy = 64.Substituting x + y = 16, we get:x = 8 and y = 8Therefore, the two numbers are 8 and 8.

Find Two Positive Numbers Whose Sum Is 16 Such That