I would like to know if my code is correct for the following question and pls edit the part where its giving an error

Question : Discrete Optimization: Consider each of the three levels for each of the five attributes

and enumerate all the possibilities in lexical order with Price as the leftmost attribute

changing slowest and taking levels sequentially $$30,$ $$10,$ $$5,$ then Time Insulated as

the left$-$second$-$most attribute changing second$-$slowest and taking values sequentially

$0\mathrm{.}5$ hrs$,1$ hr$,3$ hrs and so on$.$ You will have $243$ product candidates. $($The lexical order

produces indices as shown in mugs$-$products$-$lexical$-$order.csv$.$ Please make sure

you list your products in that exact same order. The lexical order of products is

obtained by looping as shown in mugs$-$products$-$lexical$-$order$-$loop.R$,$ which has

close similarity in python. Again, using the compensatory rule, compute and report

the following four columns of numbers for each candidate: the share, the cost, the

margin and the expected profit per person $($all under the current competition

incumbents$).$ The table that you submit needs to have all $243$ rows. Hint to check your

answer: product candidate $230$ has a negative expected profit per customer of between

$-1\mathrm{.}75$ and $-1\mathrm{.}85,$ and product candidate $106$ has an expected profit per customer of

between $0\mathrm{.}7$ and $0\mathrm{.}8.$

Code :

import numpy as np

# Define the incumbents' attributes

incumbent$\_$attributes $=[$

$(\text{'}$$$30\text{'},\text{'}3$ hrs$\text{'},\text{'}20$ oz$\text{'},$ 'Clean Easy', 'Leak resistant', 'Brand A$\text{'}),$

$(\text{'}$$$10\text{'},\text{'}1$ hrs$\text{'},\text{'}20$ oz$\text{'},$ 'Clean Fair', 'Spill resistant', 'Brand B$\text{'}),$

$(\text{'}$$$30\text{'},\text{'}1$ hrs$\text{'},\text{'}20$ oz$\text{'},$ 'Clean Easy', 'Leak resistant', 'Brand C$\text{'})$

$]$

# Define the scaling constant

c $=0\mathrm{.}0139$

# Define the attribute levels

attribute$\_$levels $=[$

$[\text{'}$$$30\text{'},\text{'}$$$10\text{'},\text{'}$$$5\text{'}],$

$[\text{'}0\mathrm{.}5$ hrs$\text{'},\text{'}1$ hrs$\text{'},\text{'}3$ hrs$\text{'}],$

$[\text{'}12$ oz$\text{'},\text{'}20$ oz$\text{'},\text{'}32$ oz$\text{'}],$

$[\text{'}$Difficult $(7$ min$)\text{'},$ 'Fair $(5$ min$)\text{'},$ 'Easy $(2$ min$)\text{'}],$

$[\text{'}$Slosh resistant', 'Spill resistant', 'Leak resistant'$],$

$[\text{'}$Brand A$\text{'},$ 'Brand B$\text{'},$ 'Brand C$\text{'}]$

$]$

# Initialize the part$-$worth utility matrix

part$\_$worth$\_$utilities $=$ np$.$zeros$((5,3))$

# Function to compute utility

def compute$\_$utility$($candidate$,$ incumbent$)$:

diff $=$ sum$($c $*($candidate$[$a$]==$ incumbent$[$a$])$ for a in range$(5))-$ sum$($c $*($candidate$[$a$]!=$ incumbent$[$a$])$ for a in range$(5))$

return $1/(1+$ np$.$exp$(-$diff$))$

# Generate candidate attributes and compute utilities

for i$,$ price in enumerate$($attribute$\_$levels$[0])$:

for j$,$ time in enumerate$($attribute$\_$levels$[1])$:

for k$,$ capacity in enumerate$($attribute$\_$levels$[2])$:

for l$,$ cleanability in enumerate$($attribute$\_$levels$[3])$:

for m$,$ containment in enumerate$($attribute$\_$levels$[4])$:

for n$,$ brand in enumerate$($attribute$\_$levels$[5])$:

# Generate candidate attributes

candidate$\_$attributes $=[$price$,$ time, capacity, cleanability, containment, brand$]$

# Compute utilities for each attribute

utilities $=[$compute$\_$utility$($candidate$\_$attributes, incumbent$)$ for incumbent in incumbent$\_$attributes$]$

# Average utility for the candidate product

avg$\_$utility $=$ np$.$mean$($utilities$)$

# Update part$-$worth utilities matrix

for a in range$(5)$:

part$\_$worth$\_$utilities$[$a$,$ n$]+=$ avg$\_$utility

# Normalize the part$-$worth utilities by the number of combinations

num$\_$combinations $=$ len$($attribute$\_$levels$[0])*$ len$($attribute$\_$levels$[1])*$ len$($attribute$\_$levels$[2])*$ len$($attribute$\_$levels$[3])*$ len$($attribute$\_$levels$[4])$

part$\_$worth$\_$utilities $/=$ num$\_$combinations

print$($part$\_$worth$\_$utilities$)$

cleanability$\_$mapping $=\{$

'Difficult': 'Difficult $(7$ min$)\text{'},$

'Fair': 'Fair $(5$ min$)\text{'},$

'Easy': 'Easy $(2$ min$)\text{'}$

$\}$

# Import the dataset

df $=$ pd$.$read$\_$csv$(\text{'}$mugs$-$products$-$lexical$-$order.csv$\text{'})$

# Define the levels for each attribute

price$\_$levels $=[\text{'}$$$30\text{'},\text{'}$$$10\text{'},\text{'}$$$5\text{'}]$

time$\_$insulated$\_$levels $=[\text{'}0\mathrm{.}5$ hrs$\text{'},\text{'}1$ hr$\text{'},\text{'}3$ hrs$\text{'}]$

# Modified calculate$\_$metrics function using the previously defined utility and cost calculation logic

def calculate$\_$metrics$($price$,$ time$\_$insulated, capacity, cleanability, containment, brand$)$:

candidate $=[$price$,$ time$\_$insulated, capacity, cleanability, containment, brand$]$

utilities $=[$compute$\_$utility$($candidate$,$ incumbent$)$ for incumbent in incumbent$\_$attributes$]$

share $=$ exp$($np$.$mean$($utilities$))/(1+$ sum$($exp$($u$)$ for u in utilities$))$

cost $=$ costs$[\text{'}$time$\_$insulated'$][$time$\_$insulated$]+$ costs$[\text{'}$capacity$\text{'}][$capacity$]+$ costs$[\text{'}$cleanability$\text{'}][$cleanability$]+$ costs$[\text{'}$containment$\text{'}][$containment$]$

margin $=$ float$($price$[1$:$])-$ cost

expected$\_$profit$\_$per$\_$person $=$ share $*$ margin

return share, cost, margin, expected$\_$profit$\_$per$\_$person

# Loop through the dataset

for index, row in df$.$iterrows$()$:

# Access data for each attribute

price $=$ row$[\text{'}$ $$30\text{'}].$strip$()$

time$\_$insulated $=$ row$[\text{'}0\mathrm{.}5$ hrs$\text{'}].$strip$()$

capacity $=$ row$[\text{'}12$ oz$\text{'}].$strip$($