In [1]:

```
# Setting up
from pulp import *
prob = LpProblem('prob', LpMinimize)
```

In [2]:

```
L = ['L'+str(i+1) for i in range(3)]
N = ['A'+str(i+1) for i in range(5)]
```

In [3]:

```
C = {'L1': 5, 'L2':10, 'L3':3} # Cost dictionary
A = {'L1': {'A1':1, 'A3':1, 'A5':1}, # Coverage dictionary
'L2': {'A2':1, 'A5':1},
'L3': {'A1':1, 'A2':1, 'A3':1, 'A4':1}}
```

There are perhaps several way to define our coverage table - in our case, we chose to use a nested dictionary, with a value of 1 for the Station/Neighborhood pairs where coverage is available.

In [4]:

```
# Declaring decision variables.
x = LpVariable.dicts('x', L, lowBound = 0, upBound = 1, cat = LpInteger)
y = LpVariable.dicts('y', N, lowBound = 0, upBound = 1, cat = LpInteger)
```

The decision variables in our problem are Boolean - we will therefore model them as integers, with a minimum value of 0, and a maximum value of 1.

In [5]:

```
# Declaring objectives
prob += lpSum([C[i]*x[i] for i in L])
for i in L:
for j in N:
if j in A[i]:
prob += A[i][j]*x[i] <= y[j]
for j in N:
prob += y[j] <= lpSum(A[i][j]*x[i] for i in L if j in A[i] if i in A.keys() )
for j in N:
prob += y[j] == 1
```

In [6]:

```
# Solving problem
prob.solve()
print('Total cost:', prob.objective.value())
print('')
print('Established Stations:\n')
for v in list(x.values()):
if v.varValue == 1:
print(f' - {v.name.replace("x_","")} ')
```

Everything in this notebook should be familiar to you, with the exception of the code that was used to iterate through the values in our list of decision variables.

In [7]:

```
list(x.values())
```

Out[7]:

As we can see in the above cell, `list(x.values())`

can be used to obtain a list of our decision variable objects. This means that we can access each one directly using an iteration, or a direct call, such as this:

In [8]:

```
list(x.values())[0]
```

Out[8]:

To obtain the value that was obtained by our solver, we need to access the `varValue`

property of our decision variable object:

In [9]:

```
list(x.values())[0].varValue
```

Out[9]:

```
from pulp import *
prob = LpProblem('prob', LpMaximize)
S = [str(i+1) for i in range(4)]
revenues = [1000, 7000, 3000, 250]
weights = [ 50, 450, 100, 20]
volumes = [ 0.5, 1, 2, 0.1]
R = dict(zip(S, revenues))
W = dict(zip(S, weights))
V = dict(zip(S, volumes))
W_max = 16200
V_max = 32
x = LpVariable.dicts('x', S, lowBound = 0, cat = LpInteger)
prob += lpSum([R[i]*x[i] for i in S])
for i in S:
prob += lpSum([W[i]*x[i] for i in S]) <= W_max
prob += lpSum([V[i]*x[i] for i in S]) <= V_max
prob.solve()
for v in prob.variables():
print(f' - Type {v.name.replace("x_","")} x {int(v.varValue):2}')
print('')
print('Total Revenue:', prob.objective.value())
```