## Step 1: Define the optimization problem
The problem is to maximize the objective function: $4.27 \times lemons + 7.35 \times chicken\ thighs + 1.78 \times corn\ cobs + 6.68 \times cheeseburgers$.

## Step 2: List all the constraints
The constraints are:
- $4.64 \times lemons + 8.84 \times chicken\ thighs + 9.92 \times corn\ cobs + 7.71 \times cheeseburgers \leq 236$ (carbohydrates)
- $4.0 \times lemons + 6.51 \times chicken\ thighs + 5.58 \times corn\ cobs + 1.41 \times cheeseburgers \leq 233$ (calcium)
- $8.84 \times chicken\ thighs + 9.92 \times corn\ cobs + 7.71 \times cheeseburgers \geq 32$ (carbohydrates from chicken thighs, corn cobs, cheeseburgers)
- $4.64 \times lemons + 8.84 \times chicken\ thighs + 9.92 \times corn\ cobs \geq 32$ (carbohydrates from lemons, chicken thighs, corn cobs)
- $4.64 \times lemons + 8.84 \times chicken\ thighs + 7.71 \times cheeseburgers \geq 32$ (carbohydrates from lemons, chicken thighs, cheeseburgers)
- $8.84 \times chicken\ thighs + 9.92 \times corn\ cobs + 7.71 \times cheeseburgers \geq 52$ (carbohydrates from chicken thighs, corn cobs, cheeseburgers)
- $4.64 \times lemons + 8.84 \times chicken\ thighs + 9.92 \times corn\ cobs \geq 52$ (carbohydrates from lemons, chicken thighs, corn cobs)
- $4.64 \times lemons + 8.84 \times chicken\ thighs + 7.71 \times cheeseburgers \geq 52$ (carbohydrates from lemons, chicken thighs, cheeseburgers)
- $8.84 \times chicken\ thighs + 9.92 \times corn\ cobs + 7.71 \times cheeseburgers \geq 47$ (carbohydrates from chicken thighs, corn cobs, cheeseburgers)
- $4.64 \times lemons + 8.84 \times chicken\ thighs + 9.92 \times corn\ cobs \geq 47$ (carbohydrates from lemons, chicken thighs, corn cobs)
- $4.64 \times lemons + 8.84 \times chicken\ thighs + 7.71 \times cheeseburgers \geq 47$ (carbohydrates from lemons, chicken thighs, cheeseburgers)
- $6.51 \times chicken\ thighs + 5.58 \times corn\ cobs \geq 49$ (calcium from chicken thighs, corn cobs)
- $4.0 \times lemons + 6.51 \times chicken\ thighs + 1.41 \times cheeseburgers \geq 43$ (calcium from lemons, chicken thighs, cheeseburgers)
- $6.51 \times chicken\ thighs + 5.58 \times corn\ cobs + 1.41 \times cheeseburgers \geq 43$ (calcium from chicken thighs, corn cobs, cheeseburgers)
- $4.0 \times lemons + 6.51 \times chicken\ thighs + 1.41 \times cheeseburgers \geq 47$ (calcium from lemons, chicken thighs, cheeseburgers)
- $6.51 \times chicken\ thighs + 5.58 \times corn\ cobs + 1.41 \times cheeseburgers \geq 47$ (calcium from chicken thighs, corn cobs, cheeseburgers)
- $9.92 \times corn\ cobs + 7.71 \times cheeseburgers \leq 196$ (carbohydrates from corn cobs, cheeseburgers)
- $4.64 \times lemons + 7.71 \times cheeseburgers \leq 190$ (carbohydrates from lemons, cheeseburgers)
- $4.64 \times lemons + 8.84 \times chicken\ thighs + 7.71 \times cheeseburgers \leq 236$ (carbohydrates from lemons, chicken thighs, cheeseburgers)
- $4.64 \times lemons + 8.84 \times chicken\ thighs + 9.92 \times corn\ cobs \leq 204$ (carbohydrates from lemons, chicken thighs, corn cobs)
- $4.64 \times lemons + 8.84 \times chicken\ thighs + 9.92 \times corn\ cobs + 7.71 \times cheeseburgers \leq 204$ (carbohydrates from all)
- $4.0 \times lemons + 5.58 \times corn\ cobs \leq 60$ (calcium from lemons, corn cobs)
- $4.0 \times lemons + 6.51 \times chicken\ thighs \leq 69$ (calcium from lemons, chicken thighs)
- $4.0 \times lemons + 1.41 \times cheeseburgers \leq 163$ (calcium from lemons, cheeseburgers)
- $4.0 \times lemons + 6.51 \times chicken\ thighs + 5.58 \times corn\ cobs \leq 94$ (calcium from lemons, chicken thighs, corn cobs)
- $4.0 \times lemons + 5.58 \times corn\ cobs + 1.41 \times cheeseburgers \leq 136$ (calcium from lemons, corn cobs, cheeseburgers)
- $6.51 \times chicken\ thighs + 5.58 \times corn\ cobs + 1.41 \times cheeseburgers \leq 169$ (calcium from chicken thighs, corn cobs, cheeseburgers)
- $4.0 \times lemons + 6.51 \times chicken\ thighs + 1.41 \times cheeseburgers \leq 211$ (calcium from lemons, chicken thighs, cheeseburgers)
- $4.0 \times lemons + 6.51 \times chicken\ thighs + 5.58 \times corn\ cobs + 1.41 \times cheeseburgers \leq 211$ (calcium from all)

## Step 3: Implement the optimization problem using Gurobi
We will use the Gurobi library in Python to solve this optimization problem.

```python
import gurobi

# Define the model
model = gurobi.Model()

# Define the variables
lemons = model.addVar(name="lemons", vtype=gurobi.GRB.INTEGER, lb=0)
chicken_thighs = model.addVar(name="chicken_thighs", vtype=gurobi.GRB.INTEGER, lb=0)
corn_cobs = model.addVar(name="corn_cobs", vtype=gurobi.GRB.CONTINUOUS, lb=0)
cheeseburgers = model.addVar(name="cheeseburgers", vtype=gurobi.GRB.CONTINUOUS, lb=0)

# Define the objective function
model.setObjective(4.27 * lemons + 7.35 * chicken_thighs + 1.78 * corn_cobs + 6.68 * cheeseburgers, gurobi.GRB.MAXIMIZE)

# Define the constraints
model.addConstr(4.64 * lemons + 8.84 * chicken_thighs + 9.92 * corn_cobs + 7.71 * cheeseburgers <= 236)
model.addConstr(4.0 * lemons + 6.51 * chicken_thighs + 5.58 * corn_cobs + 1.41 * cheeseburgers <= 233)

model.addConstr(8.84 * chicken_thighs + 9.92 * corn_cobs + 7.71 * cheeseburgers >= 32)
model.addConstr(4.64 * lemons + 8.84 * chicken_thighs + 9.92 * corn_cobs >= 32)
model.addConstr(4.64 * lemons + 8.84 * chicken_thighs + 7.71 * cheeseburgers >= 32)

model.addConstr(8.84 * chicken_thighs + 9.92 * corn_cobs + 7.71 * cheeseburgers >= 52)
model.addConstr(4.64 * lemons + 8.84 * chicken_thighs + 9.92 * corn_cobs >= 52)
model.addConstr(4.64 * lemons + 8.84 * chicken_thighs + 7.71 * cheeseburgers >= 52)

model.addConstr(8.84 * chicken_thighs + 9.92 * corn_cobs + 7.71 * cheeseburgers >= 47)
model.addConstr(4.64 * lemons + 8.84 * chicken_thighs + 9.92 * corn_cobs >= 47)
model.addConstr(4.64 * lemons + 8.84 * chicken_thighs + 7.71 * cheeseburgers >= 47)

model.addConstr(6.51 * chicken_thighs + 5.58 * corn_cobs >= 49)
model.addConstr(4.0 * lemons + 6.51 * chicken_thighs + 1.41 * cheeseburgers >= 43)
model.addConstr(6.51 * chicken_thighs + 5.58 * corn_cobs + 1.41 * cheeseburgers >= 43)
model.addConstr(4.0 * lemons + 6.51 * chicken_thighs + 1.41 * cheeseburgers >= 47)
model.addConstr(6.51 * chicken_thighs + 5.58 * corn_cobs + 1.41 * cheeseburgers >= 47)

model.addConstr(9.92 * corn_cobs + 7.71 * cheeseburgers <= 196)
model.addConstr(4.64 * lemons + 7.71 * cheeseburgers <= 190)
model.addConstr(4.64 * lemons + 8.84 * chicken_thighs + 7.71 * cheeseburgers <= 236)
model.addConstr(4.64 * lemons + 8.84 * chicken_thighs + 9.92 * corn_cobs <= 204)
model.addConstr(4.64 * lemons + 8.84 * chicken_thighs + 9.92 * corn_cobs + 7.71 * cheeseburgers <= 204)

model.addConstr(4.0 * lemons + 5.58 * corn_cobs <= 60)
model.addConstr(4.0 * lemons + 6.51 * chicken_thighs <= 69)
model.addConstr(4.0 * lemons + 1.41 * cheeseburgers <= 163)
model.addConstr(4.0 * lemons + 6.51 * chicken_thighs + 5.58 * corn_cobs <= 94)
model.addConstr(4.0 * lemons + 5.58 * corn_cobs + 1.41 * cheeseburgers <= 136)
model.addConstr(6.51 * chicken_thighs + 5.58 * corn_cobs + 1.41 * cheeseburgers <= 169)
model.addConstr(4.0 * lemons + 6.51 * chicken_thighs + 1.41 * cheeseburgers <= 211)
model.addConstr(4.0 * lemons + 6.51 * chicken_thighs + 5.58 * corn_cobs + 1.41 * cheeseburgers <= 211)

# Solve the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", model.objVal)
    print("Lemons: ", lemons.varValue)
    print("Chicken Thighs: ", chicken_thighs.varValue)
    print("Corn Cobs: ", corn_cobs.varValue)
    print("Cheeseburgers: ", cheeseburgers.varValue)
else:
    print("The model is infeasible")
```