The Rod Cutting problem Given a rod of length n inches and a list of prices that contains prices of all pieces of size smaller than n. Determine the maximum value obtainable by cutting up the rod and selling the pieces. For example, if length of the rod is 8 and the values of different pieces are given as following, then the maximum obtainable value is 22 (by cutting in two pieces of lengths 2 and 6)
length   | 1   2   3   4   5   6   7   8  
-------------------------------------------
price    | 1   5   8   9  10  17  17  20

And if the prices are as following, then the maximum obtainable value is 24 (by cutting in eight pieces of length 1)
length   | 1   2   3   4   5   6   7   8  
--------------------------------------------
price    | 3   5   8   9  10  17  17  20

The input will be given in this form:
The prices will be in ascending order, index starting at 1 to n separated by a space.
{price of length 1} {price of length 2}.... {price of length N}
The output should be the maximum Obtainable Value
{maxVal}
a Non-Golfed solution to this, in Python is:
INT_MIN = -32767
def cutRod(price, n): 
    val = [0 for x in range(n+1)] 
    val[0] = 0
    for i in range(1, n+1): 
        max_val = INT_MIN 
        for j in range(i): 
             max_val = max(max_val, price[j] + val[i-j-1]) 
        val[i] = max_val 
  
    return val[n] 
  
arr = [1,2,3,4,5,6,7,8,9,10] 
size = len(arr) 
print(cutRod(arr, size))

Test cases:
|                                      Input                                     | Output |
|:------------------------------------------------------------------------------:|:------:|
|                              `1 5 8 9 10 17 17 20`                             |  `22`  |
|                                `1 3 2 5 6 7 4 8`                               |  `12`  |
|                     `5 6 3 2 4 6 8 7 3 4 6 2 12 4 5 7 4 3`                     |  `90`  |
| `23 2 3 45 34 23 3143 13 13 213 1321 3123 12 312 312 31 3 213 432 41 3 123 43` | `9475` |
Jelly, 7 bytes
LŒṗịµ§Ṁ
L        length
 Œṗ      integer partitions
   ị     index
     §Ṁ  sum each and take the maximum

My first jelly answer, so there can probably be improvements made.
Try it online!