Looping over data frame to cap and sum another data frame

I am trying to use entries from df1 to limit amounts in df2, then add them up based on their type and summarize in df3. I'm not sure how to get it, the for loop using iterrows would be my best guess but it's not complete.

Code:

import numpy as np
import pandas as pd

df1 = pd.DataFrame({'Caps':['25','50','100']})
df2 = pd.DataFrame({'Amounts':['45','25','65','35','85','105','80'], \
                    'Type':   ['a' ,'b' ,'b' ,'c' ,'a' , 'b' ,'d' ]})
df3 = pd.DataFrame({'Type':   ['a' ,'b' ,'c' ,'d']})

df1['Caps'] = df1['Caps'].astype(float)
df2['Amounts'] = df2['Amounts'].astype(float)

for index1, row1 in df1.iterrows():
    for index2, row2 in df3.iterrows():
        df3[str(row1['Caps']+'limit')] = df2['Amounts'].where(
            df2['Type'] == row2['Type']).where(
            df2['Amounts']<= row1['Caps'], row1['Caps']).sum()


# My ideal output would be this:

df3 = pd.DataFrame({'Type':['a','b','c','d'],
                    'Total':['130','195','35','80'],
                    '25limit':['50','75','25','25'],
                    '50limit':['95','125','35','50'],
                    '100limit':['130','190','35','80'],
                    })

Output:

>>> df3

  Type Total 25limit 50limit 100limit
0    a   130      50      95      130
1    b   195      75     125      190
2    c    35      25      35       35
3    d    80      25      50       80

Use numpy for compare all values Amounts with Caps by broadcasting to 2d array a, then create DataFrame by constructor with sum per columns, transpose by DataFrame.T and DataFrame.add_prefix.

For aggregated column use DataFrame.insert for first column with GroupBy.sum:

df1['Caps'] = df1['Caps'].astype(int)
df2['Amounts'] = df2['Amounts'].astype(int)

am = df2['Amounts'].to_numpy()
ca = df1['Caps'].to_numpy()
#pandas below 0.24
#am = df2['Amounts'].values
#ca = df1['Caps'].values
a  = np.where(am <= ca[:, None], am[None, :], ca[:, None])

df1 = (pd.DataFrame(a,columns=df2['Type'],index=df1['Caps'])
         .sum(axis=1, level=0).T.add_suffix('limit'))
df1.insert(0, 'Total', df2.groupby('Type')['Amounts'].sum())
df1 = df1.reset_index().rename_axis(None, axis=1)
print (df1)
  Type  Total  25limit  50limit  100limit
0    a    130       50       95       130
1    b    195       75      125       190
2    c     35       25       35        35
3    d     80       25       50        80

Here is my solution without numpy, however it is two times slower than @jezrael's solution, 10.5ms vs. 5.07ms.

limcols= df1.Caps.to_list()
df2=df2.reindex(columns=["Amounts","Type"]+limcols)

df2[limcols]= df2[limcols].transform( \
                  lambda sc: np.where(df2.Amounts.le(sc.name),df2.Amounts,sc.name))

# Summations:
g=df2.groupby("Type")
df3= g[limcols].sum()
df3.insert(0,"Total", g.Amounts.sum())

# Renaming columns:
c_dic={ lim:f"{lim:.0f}limit" for lim in limcols}
df3= df3.rename(columns=c_dic).reset_index()

# Cleanup:
#df2=df2.drop(columns=limcols)