Question

split 20 into two nonnegative numbers x,y such that the product of x and y^2 is a maximum

Answer 1

>>> for i in range(21):
x = i
y = 20 - i
print(x, '*', y, '^2 =', x * y**2)


0 * 20 ^2 = 0
1 * 19 ^2 = 361
2 * 18 ^2 = 648
3 * 17 ^2 = 867
4 * 16 ^2 = 1024
5 * 15 ^2 = 1125
6 * 14 ^2 = 1176
7 * 13 ^2 = 1183
8 * 12 ^2 = 1152
9 * 11 ^2 = 1089
10 * 10 ^2 = 1000
11 * 9 ^2 = 891
12 * 8 ^2 = 768
13 * 7 ^2 = 637
14 * 6 ^2 = 504
15 * 5 ^2 = 375
16 * 4 ^2 = 256
17 * 3 ^2 = 153
18 * 2 ^2 = 72
19 * 1 ^2 = 19
20 * 0 ^2 = 0