Here's the formulation of the linear program and the Gurobi code to solve it:

**Decision Variables:**

* `x`: Acres of peas to plant
* `y`: Acres of beans to plant

**Objective Function:**

Maximize profit: `100x + 160y`

**Constraints:**

* **Land Constraint:** `x + y <= 30` (Total acres available)
* **Bug Spray Constraint:** `30x + 50y <= 1300` (Budget for bug spray)
* **Care-taking Constraint:** `2x + 1.5y <= 50` (Available hours for care-taking)
* **Non-negativity Constraints:** `x >= 0`, `y >= 0`

```python
import gurobipy as gp
from gurobipy import GRB

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

# Create decision variables
x = m.addVar(lb=0, name="peas")  # Acres of peas
y = m.addVar(lb=0, name="beans") # Acres of beans

# Set objective function
m.setObjective(100*x + 160*y, GRB.MAXIMIZE)

# Add constraints
m.addConstr(x + y <= 30, "land")
m.addConstr(30*x + 50*y <= 1300, "bug_spray")
m.addConstr(2*x + 1.5*y <= 50, "care_taking")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print(f"Optimal Solution Found:")
    print(f"Plant {x.x:.2f} acres of peas")
    print(f"Plant {y.x:.2f} acres of beans")
    print(f"Maximum Profit: ${m.objVal:.2f}")
elif m.status == GRB.INFEASIBLE:
    print("The model is infeasible.")
else:
    print(f"Optimization terminated with status {m.status}")

```
