Question 261753
Let A and B be the two non negative numbers.
(i) {{{A + B = 20}}}
(ii) {{{2A * B^2 = max}}}
step 1 - solve for A to get
(iii) {{{A = 20 - B}}}
step 2 - substitute (ii) into (i) to get
(iv) {{{2(20-B) * B^2}}}
step 3 - simplified we get
(v) {{{-2B^3 + 40B^2}}}
step 4 - take a derivative and set = 0 to get
(vi) {{{(-6B^2+80B) = 0}}}
step 5 - factor to get
(vii) {{{(-2B(3B - 40)) = 0}}}
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