SOLUTION: Find two non negative numbers whose sum is 20 and for which the product of twice one number and the square of the other number will be a maximum.

Question 261753: Find two non negative numbers whose sum is 20 and for which the product of twice one number and the square of the other number will be a maximum.
Answer by drk(1908) (Show Source): You can put this solution on YOUR website!
Let A and B be the two non negative numbers.
(i)
(ii)
step 1 - solve for A to get
(iii)
step 2 - substitute (ii) into (i) to get
(iv)
step 3 - simplified we get
(v)
step 4 - take a derivative and set = 0 to get
(vi)
step 5 - factor to get
(vii)
We get
B = 0 or B = 13.3333
The closest integer to this is
B =13
so A = 7.
--
7+13 = 20
2*7 * 13^2 = 2366
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