## Step 1: Define the variables and their attributes
We have four variables: 'pathfinder teams', 'artillery batteries', 'CBRN platoons', and 'logistics companies'. Each variable has two attributes: 'mobility rating' and 'offensive capability rating'. The attributes for each variable are given as follows:
- 'pathfinder teams': mobility rating = 16, offensive capability rating = 1
- 'artillery batteries': mobility rating = 8, offensive capability rating = 9
- 'CBRN platoons': mobility rating = 10, offensive capability rating = 6
- 'logistics companies': mobility rating = 15, offensive capability rating = 13

## Step 2: Formulate the objective function
The objective function to maximize is: $5 \times \text{pathfinder teams} + 3 \times \text{artillery batteries} + 5 \times \text{CBRN platoons} + 8 \times \text{logistics companies}$

## 3: Define the constraints
1. $\text{mobility rating from artillery batteries} + \text{mobility rating from logistics companies} \geq 45$
$8 \times \text{artillery batteries} + 15 \times \text{logistics companies} \geq 45$

2. $\text{mobility rating from pathfinder teams} + \text{mobility rating from CBRN platoons} \geq 43$
$16 \times \text{pathfinder teams} + 10 \times \text{CBRN platoons} \geq 43$

3. $\text{mobility rating from artillery batteries} + \text{mobility rating from CBRN platoons} \geq 49$
$8 \times \text{artillery batteries} + 10 \times \text{CBRN platoons} \geq 49$

4. $\text{mobility rating from artillery batteries} + \text{mobility rating from CBRN platoons} + \text{mobility rating from logistics companies} \geq 58$
$8 \times \text{artillery batteries} + 10 \times \text{CBRN platoons} + 15 \times \text{logistics companies} \geq 58$

5. $\text{mobility rating from pathfinder teams} + \text{mobility rating from CBRN platoons} + \text{mobility rating from logistics companies} \geq 58$
$16 \times \text{pathfinder teams} + 10 \times \text{CBRN platoons} + 15 \times \text{logistics companies} \geq 58$

6. $\text{mobility rating from artillery batteries} + \text{mobility rating from CBRN platoons} + \text{mobility rating from logistics companies} \geq 41$
$8 \times \text{artillery batteries} + 10 \times \text{CBRN platoons} + 15 \times \text{logistics companies} \geq 41$

7. $\text{mobility rating from pathfinder teams} + \text{mobility rating from CBRN platoons} + \text{mobility rating from logistics companies} \geq 41$
$16 \times \text{pathfinder teams} + 10 \times \text{CBRN platoons} + 15 \times \text{logistics companies} \geq 41$

8. $\text{offensive capability rating from artillery batteries} + \text{offensive capability rating from CBRN platoons} \geq 62$
$9 \times \text{artillery batteries} + 6 \times \text{CBRN platoons} \geq 62$

9. $\text{offensive capability rating from artillery batteries} + \text{offensive capability rating from logistics companies} \geq 66$
$9 \times \text{artillery batteries} + 13 \times \text{logistics companies} \geq 66$

10. $\text{offensive capability rating from pathfinder teams} + \text{offensive capability rating from logistics companies} \geq 36$
$1 \times \text{pathfinder teams} + 13 \times \text{logistics companies} \geq 36$

11. $\text{offensive capability rating from CBRN platoons} + \text{offensive capability rating from logistics companies} \geq 74$
$6 \times \text{CBRN platoons} + 13 \times \text{logistics companies} \geq 74$

12. $\text{mobility rating from pathfinder teams} + \text{mobility rating from logistics companies} \leq 123$
$16 \times \text{pathfinder teams} + 15 \times \text{logistics companies} \leq 123$

13. $\text{mobility rating from artillery batteries} + \text{mobility rating from logistics companies} \leq 161$
$8 \times \text{artillery batteries} + 15 \times \text{logistics companies} \leq 161$

14. $\text{mobility rating from pathfinder teams} + \text{mobility rating from artillery batteries} \leq 215$
$16 \times \text{pathfinder teams} + 8 \times \text{artillery batteries} \leq 215$

15. $\text{mobility rating from pathfinder teams} + \text{mobility rating from artillery batteries} + \text{mobility rating from CBRN platoons} + \text{mobility rating from logistics companies} \leq 215$
$16 \times \text{pathfinder teams} + 8 \times \text{artillery batteries} + 10 \times \text{CBRN platoons} + 15 \times \text{logistics companies} \leq 215$

16. $\text{offensive capability rating from pathfinder teams} + \text{offensive capability rating from CBRN platoons} \leq 220$
$1 \times \text{pathfinder teams} + 6 \times \text{CBRN platoons} \leq 220$

17. $\text{offensive capability rating from pathfinder teams} + \text{offensive capability rating from logistics companies} \leq 113$
$1 \times \text{pathfinder teams} + 13 \times \text{logistics companies} \leq 113$

18. $\text{offensive capability rating from artillery batteries} + \text{offensive capability rating from logistics companies} \leq 141$
$9 \times \text{artillery batteries} + 13 \times \text{logistics companies} \leq 141$

19. $\text{offensive capability rating from CBRN platoons} + \text{offensive capability rating from logistics companies} \leq 329$
$6 \times \text{CBRN platoons} + 13 \times \text{logistics companies} \leq 329$

20. $\text{offensive capability rating from pathfinder teams} + \text{offensive capability rating from artillery batteries} + \text{offensive capability rating from CBRN platoons} + \text{offensive capability rating from logistics companies} \leq 329$
$1 \times \text{pathfinder teams} + 9 \times \text{artillery batteries} + 6 \times \text{CBRN platoons} + 13 \times \text{logistics companies} \leq 329$

## 4: Implement the problem in Gurobi
```python
import gurobi

# Create a new Gurobi model
m = gurobi.Model()

# Define the variables
pathfinder_teams = m.addVar(name="pathfinder_teams", vtype=gurobi.GRB.INTEGER)
artillery_batteries = m.addVar(name="artillery_batteries", vtype=gurobi.GRB.INTEGER)
CBRN_platoons = m.addVar(name="CBRN_platoons", vtype=gurobi.GRB.INTEGER)
logistics_companies = m.addVar(name="logistics_companies", vtype=gurobi.GRB.INTEGER)

# Define the objective function
m.setObjective(5 * pathfinder_teams + 3 * artillery_batteries + 5 * CBRN_platoons + 8 * logistics_companies, gurobi.GRB.MAXIMIZE)

# Add constraints
m.addConstr(8 * artillery_batteries + 15 * logistics_companies >= 45)
m.addConstr(16 * pathfinder_teams + 10 * CBRN_platoons >= 43)
m.addConstr(8 * artillery_batteries + 10 * CBRN_platoons >= 49)
m.addConstr(8 * artillery_batteries + 10 * CBRN_platoons + 15 * logistics_companies >= 58)
m.addConstr(16 * pathfinder_teams + 10 * CBRN_platoons + 15 * logistics_companies >= 58)
m.addConstr(8 * artillery_batteries + 10 * CBRN_platoons + 15 * logistics_companies >= 41)
m.addConstr(16 * pathfinder_teams + 10 * CBRN_platoons + 15 * logistics_companies >= 41)
m.addConstr(9 * artillery_batteries + 6 * CBRN_platoons >= 62)
m.addConstr(9 * artillery_batteries + 13 * logistics_companies >= 66)
m.addConstr(pathfinder_teams + 13 * logistics_companies >= 36)
m.addConstr(6 * CBRN_platoons + 13 * logistics_companies >= 74)
m.addConstr(16 * pathfinder_teams + 15 * logistics_companies <= 123)
m.addConstr(8 * artillery_batteries + 15 * logistics_companies <= 161)
m.addConstr(16 * pathfinder_teams + 8 * artillery_batteries <= 215)
m.addConstr(16 * pathfinder_teams + 8 * artillery_batteries + 10 * CBRN_platoons + 15 * logistics_companies <= 215)
m.addConstr(pathfinder_teams + 6 * CBRN_platoons <= 220)
m.addConstr(pathfinder_teams + 13 * logistics_companies <= 113)
m.addConstr(9 * artillery_batteries + 13 * logistics_companies <= 141)
m.addConstr(6 * CBRN_platoons + 13 * logistics_companies <= 329)
m.addConstr(pathfinder_teams + 9 * artillery_batteries + 6 * CBRN_platoons + 13 * logistics_companies <= 329)

# Optimize the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("Pathfinder Teams: ", pathfinder_teams.varValue)
    print("Artillery Batteries: ", artillery_batteries.varValue)
    print("CBRN Platoons: ", CBRN_platoons.varValue)
    print("Logistics Companies: ", logistics_companies.varValue)
else:
    print("The model is infeasible")
```