```json
{
  "sym_variables": [
    ("x0", "carrots"),
    ("x1", "sunflowers"),
    ("x2", "lilies"),
    ("x3", "carnations"),
    ("x4", "potato vines")
  ],
  "objective_function": "5*x0 + 9*x1 + 8*x2 + 5*x3 + 7*x4",
  "constraints": [
    "7*x2 + 1*x4 >= 11",
    "4*x1 + 5*x2 >= 15",
    "2*x3 + 1*x4 >= 20",
    "4*x1 + 5*x2 + 2*x3 >= 12",
    "7*x0 + 2*x3 + 1*x4 >= 12",
    "7*x0 + 5*x2 + 2*x3 >= 12",
    "7*x0 + 4*x1 + 5*x2 >= 12",
    "7*x0 + 4*x1 + 2*x3 >= 12",
    "4*x1 + 5*x2 + 2*x3 >= 16",
    "7*x0 + 2*x3 + 1*x4 >= 16",
    "7*x0 + 5*x2 + 2*x3 >= 16",
    "7*x0 + 4*x1 + 5*x2 >= 16",
    "7*x0 + 4*x1 + 2*x3 >= 16",
    "4*x1 + 5*x2 + 2*x3 >= 16",
    "7*x0 + 2*x3 + 1*x4 >= 16",
    "7*x0 + 5*x2 + 2*x3 >= 16",
    "7*x0 + 4*x1 + 5*x2 >= 16",
    "7*x0 + 4*x1 + 2*x3 >= 16",
    "4*x1 + 5*x2 + 2*x3 >= 20",
    "7*x0 + 2*x3 + 1*x4 >= 20",
    "7*x0 + 5*x2 + 2*x3 >= 20",
    "7*x0 + 4*x1 + 5*x2 >= 20",
    "7*x0 + 4*x1 + 2*x3 >= 20",
    "4*x1 + 5*x2 + 2*x3 >= 19",
    "7*x0 + 2*x3 + 1*x4 >= 19",
    "7*x0 + 5*x2 + 2*x3 >= 19",
    "7*x0 + 4*x1 + 5*x2 >= 19",
    "7*x0 + 4*x1 + 2*x3 >= 19",
    "7*x0 + 5*x3 >= 27",
    "7*x0 + 4*x4 >= 18",
    "5*x3 + 4*x4 >= 24",
    "7*x0 + 8*x2 + 5*x3 >= 29",
    "1*x1 + 8*x2 + 5*x3 >= 29",
    "7*x0 + 1*x1 + 8*x2 >= 29",
    "7*x0 + 8*x2 + 5*x3 >= 25",
    "1*x1 + 8*x2 + 5*x3 >= 25",
    "7*x0 + 1*x1 + 8*x2 >= 25",
    "7*x0 + 8*x2 + 5*x3 >= 26",
    "1*x1 + 8*x2 + 5*x3 >= 26",
    "7*x0 + 1*x1 + 8*x2 >= 26",
    "5*x2 + 2*x3 <= 70",
    "4*x1 + 2*x3 <= 81",
    "7*x0 + 1*x4 <= 95",
    "5*x2 + 1*x4 <= 79",
    "7*x0 + 4*x1 + 5*x2 + 2*x3 + 1*x4 <= 79",
    "7*x0 + 1*x1 <= 82",
    "1*x1 + 4*x4 <= 56",
    "1*x1 + 5*x3 <= 146",
    "8*x2 + 4*x4 <= 129",
    "1*x1 + 8*x2 + 5*x3 <= 93",
    "7*x0 + 8*x2 + 5*x3 <= 114",
    "7*x0 + 8*x2 + 4*x4 <= 29",  
    "8*x2 + 5*x3 + 4*x4 <= 149",
    "7*x0 + 1*x1 + 5*x3 <= 98",
    "7*x0 + 1*x1 + 8*x2 <= 50",
    "7*x0 + 1*x1 + 8*x2 + 5*x3 + 4*x4 <= 50",
    "7*x0 + 4*x1 + 5*x2 + 2*x3 <= 105",
    "7*x0 + 1*x1 + 8*x2 + 5*x3 + 4*x4 <= 149" 
  ]
}
```

```python
import gurobipy as gp

# Create a new model
m = gp.Model("optimization_problem")

# Create variables
carrots = m.addVar(vtype=gp.GRB.INTEGER, name="carrots")
sunflowers = m.addVar(vtype=gp.GRB.INTEGER, name="sunflowers")
lilies = m.addVar(vtype=gp.GRB.INTEGER, name="lilies")
carnations = m.addVar(vtype=gp.GRB.INTEGER, name="carnations")
potato_vines = m.addVar(vtype=gp.GRB.INTEGER, name="potato_vines")

# Set objective function
m.setObjective(5*carrots + 9*sunflowers + 8*lilies + 5*carnations + 7*potato_vines, gp.GRB.MAXIMIZE)

# Add constraints
m.addConstr(7*lilies + 1*potato_vines >= 11)
m.addConstr(4*sunflowers + 5*lilies >= 15)
m.addConstr(2*carnations + 1*potato_vines >= 20)
m.addConstr(4*sunflowers + 5*lilies + 2*carnations >= 12)
m.addConstr(7*carrots + 2*carnations + 1*potato_vines >= 12)
m.addConstr(7*carrots + 5*lilies + 2*carnations >= 12)
m.addConstr(7*carrots + 4*sunflowers + 5*lilies >= 12)
m.addConstr(7*carrots + 4*sunflowers + 2*carnations >= 12)
m.addConstr(4*sunflowers + 5*lilies + 2*carnations >= 16)
m.addConstr(7*carrots + 2*carnations + 1*potato_vines >= 16)
m.addConstr(7*carrots + 5*lilies + 2*carnations >= 16)
m.addConstr(7*carrots + 4*sunflowers + 5*lilies >= 16)
m.addConstr(7*carrots + 4*sunflowers + 2*carnations >= 16)
m.addConstr(4*sunflowers + 5*lilies + 2*carnations >= 16)
m.addConstr(7*carrots + 2*carnations + 1*potato_vines >= 16)
m.addConstr(7*carrots + 5*lilies + 2*carnations >= 16)
m.addConstr(7*carrots + 4*sunflowers + 5*lilies >= 16)
m.addConstr(7*carrots + 4*sunflowers + 2*carnations >= 16)
m.addConstr(4*sunflowers + 5*lilies + 2*carnations >= 20)
m.addConstr(7*carrots + 2*carnations + 1*potato_vines >= 20)
m.addConstr(7*carrots + 5*lilies + 2*carnations >= 20)
m.addConstr(7*carrots + 4*sunflowers + 5*lilies >= 20)
m.addConstr(7*carrots + 4*sunflowers + 2*carnations >= 20)
m.addConstr(4*sunflowers + 5*lilies + 2*carnations >= 19)
m.addConstr(7*carrots + 2*carnations + 1*potato_vines >= 19)
m.addConstr(7*carrots + 5*lilies + 2*carnations >= 19)
m.addConstr(7*carrots + 4*sunflowers + 5*lilies >= 19)
m.addConstr(7*carrots + 4*sunflowers + 2*carnations >= 19)


m.addConstr(7 * carrots + 5 * carnations >= 27)
m.addConstr(7 * carrots + 4 * potato_vines >= 18)
m.addConstr(5 * carnations + 4 * potato_vines >= 24)
m.addConstr(7 * carrots + 8 * lilies + 5 * carnations >= 29)
m.addConstr(sunflowers + 8 * lilies + 5 * carnations >= 29)
m.addConstr(7 * carrots + sunflowers + 8 * lilies >= 29)
m.addConstr(7 * carrots + 8 * lilies + 5 * carnations >= 25)
m.addConstr(sunflowers + 8 * lilies + 5 * carnations >= 25)
m.addConstr(7 * carrots + sunflowers + 8 * lilies >= 25)
m.addConstr(7 * carrots + 8 * lilies + 5 * carnations >= 26)
m.addConstr(sunflowers + 8 * lilies + 5 * carnations >= 26)
m.addConstr(7 * carrots + sunflowers + 8 * lilies >= 26)

m.addConstr(5*lilies + 2*carnations <= 70)
m.addConstr(4*sunflowers + 2*carnations <= 81)
m.addConstr(7*carrots + 1*potato_vines <= 95)
m.addConstr(5*lilies + 1*potato_vines <= 79)
m.addConstr(7*carrots + 4*sunflowers + 5*lilies + 2*carnations + 1*potato_vines <= 79)
m.addConstr(7*carrots + 1*sunflowers <= 82)
m.addConstr(1*sunflowers + 4*potato_vines <= 56)
m.addConstr(1*sunflowers + 5*carnations <= 146)
m.addConstr(8*lilies + 4*potato_vines <= 129)
m.addConstr(1*sunflowers + 8*lilies + 5*carnations <= 93)
m.addConstr(7*carrots + 8*lilies + 5*carnations <= 114)
m.addConstr(7*carrots + 8*lilies + 4*potato_vines <= 29)
m.addConstr(8*lilies + 5*carnations + 4*potato_vines <= 149)
m.addConstr(7*carrots + 1*sunflowers + 5*carnations <= 98)
m.addConstr(7*carrots + 1*sunflowers + 8*lilies <= 50)
m.addConstr(7*carrots + 1*sunflowers + 8*lilies + 5*carnations + 4*potato_vines <= 50)

m.addConstr(7*carrots + 4*sunflowers + 5*lilies + 2*carnations <= 105)
m.addConstr(7*carrots + sunflowers + 8*lilies + 5*carnations + 4*potato_vines <= 149)


# Optimize model
m.optimize()

# Print results
if m.status == gp.GRB.OPTIMAL:
    print('Obj: %g' % m.objVal)
    for v in m.getVars():
        print('%s %g' % (v.varName, v.x))
elif m.status == gp.GRB.INFEASIBLE:
    print("The model is infeasible.")
else:
    print("Optimization ended with status %d" % m.status)

```
