How to sort values in DataFrame for both numerical and string values?

I have the following pandas DataFrame with mixed data types: string and integer values. I want to sort values of this DataFrame in descending order using multiple columns: Price and Name. The string values (i.e. Name) should be sorted in the alphabetical order, or actually can be ignored at all, because the most important ones are numerical values.

The problem is that the list of target columns can contain both string and integer columns, e.g. target_columns = ["Price","Name"]

d = {'1': ['25', 'AAA', 2], '2': ['30', 'BBB', 3], '3': ['5', 'CCC', 2], \
     '4': ['300', 'DDD', 2], '5': ['30', 'DDD', 3],  '6': ['100', 'AAA', 3]}

columns=['Price', 'Name', 'Class']

target_columns = ['Price', 'Name']
order_per_cols = [False] * len(target_columns)

df = pd.DataFrame.from_dict(data=d, orient='index')
df.columns = columns
df.sort_values(list(target_columns), ascending=order_per_cols, inplace=True)

Currently, this code fails with the following message:

TypeError: '<' not supported between instances of 'str' and 'int'

The expected output:

Price    Name    Class
300      DDD     2
100      AAA     3
30       DDD     3
30       BBB     3
25       AAA     2
5        CCC     2

Copyright Notice：Content Author:「Fluxy」，Reproduced under the CC 4.0 BY-SA copyright license with a link to the original source and this disclaimer.
Link to original article：https://stackoverflow.com/questions/59164941/how-to-sort-values-in-dataframe-for-both-numerical-and-string-values