To determine which of the numbers sum up to exactly 28561.36, we need to consider subsets of the list of numbers and check if any combination of them gives the total sum of 28561.36.

Here are the numbers you provided:

1. 139.87
2. 8636.10
3. 152.99
4. 5352.08
5. 13709.51
6. 10190.68
7. 5432.78
8. 1750.00
9. 1196.67
10. 2582.35
11. 45633.54
12. 50.48
13. 1786.70

We need to check if any subset of these numbers adds up to 28561.36. Let's go ahead and do that.

itertools import combinations

Given numbers

numbers = [139.87, 8636.10, 152.99, 5352.08, 13709.51, 10190.68, 5432.78, 1750.00, 1196.67, 2582.35, 45633.54, 50.48, 1786.70]

Target sum

target_sum = 28561.36

Check all combinations of numbers to see if any sum up to the target

valid_combinations = [] for r in range(1, len(numbers) + 1): for combo in combinations(numbers, r): if abs(sum(combo) - target_sum) < 0.01: # Allowing small floating point error valid_combinations.append(combo)

valid_combinationsIt seems that none of the combinations of the given numbers add up to exactly 28561.36.

Would you like to explore another approach or check something else? Here are some related questions to deepen our exploration:

1. What happens if we round the numbers to the nearest whole number? Would any combinations then sum up to 28561.36?
2. How can we handle small rounding errors in cases like this?
3. Can we use a different mathematical method (like linear programming) to find a subset that approximates the target sum?
4. What is the process for solving subset sum problems in general?
5. How would we modify this approach if the target sum were slightly different (e.g., 28561.00)?

Tip: When dealing with floating-point precision in sums, always consider a small margin of error (e.g., 0.01) to account for potential calculation inaccuracies.