## Step 1: Define the symbolic representation of the problem
The problem involves minimizing an objective function subject to several constraints. The variables are 'strawberries', 'apple pies', 'apples', and 'peanutbutter sandwiches', which we can denote as $x_0, x_1, x_2, x_3$ respectively.

## Step 2: Convert the objective function into symbolic notation
The objective function to minimize is $5x_0 + 1x_1 + 2x_2 + 7x_3$.

## 3: List the constraints in symbolic notation
The constraints given are:
- $7x_0 + 7x_3 \geq 94$
- $18x_2 + 7x_3 \geq 43$
- $7x_0 + 7x_1 + 18x_2 \geq 53$
- $7x_0 + 7x_1 + 18x_2 + 7x_3 \geq 53$
- $35x_1 + 12x_2 \geq 28$
- $35x_1 + 23x_3 \geq 16$
- $12x_2 + 23x_3 \geq 28$
- $18x_0 + 23x_3 \geq 31$
- $18x_0 + 12x_2 \geq 38$
- $35x_1 + 12x_2 + 23x_3 \geq 35$
- $18x_0 + 35x_1 + 12x_2 \geq 35$
- $18x_0 + 35x_1 + 23x_3 \geq 35$
- $12x_2 + 23x_3 + 35x_1 \geq 26$
- $18x_0 + 35x_1 + 12x_2 \geq 26$
- $18x_0 + 35x_1 + 23x_3 \geq 26$
- $18x_0 + 12x_2 + 23x_3 \geq 26$
- $35x_1 + 12x_2 + 23x_3 \geq 23$
- $18x_0 + 35x_1 + 12x_2 \geq 23$
- $18x_0 + 35x_1 + 23x_3 \geq 23$
- $-3x_0 + 2x_1 \geq 0$
- $-x_1 + 2x_3 \geq 0$
- $18x_2 + 7x_3 \leq 113$
- $7x_0 + 18x_2 \leq 144$
- $7x_0 + 18x_2 + 7x_3 \leq 192$
- $7x_1 + 18x_2 + 7x_3 \leq 311$
- $7x_0 + 7x_1 + 18x_2 \leq 186$
- $18x_0 + 12x_2 \leq 88$

## 4: Define the symbolic variables
The symbolic variables are:
- $x_0$ for 'strawberries'
- $x_1$ for 'apple pies'
- $x_2$ for 'apples'
- $x_3$ for 'peanutbutter sandwiches'

## 5: Create the Gurobi model
We will now create a Gurobi model in Python.

```python
import gurobi

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

# Define the variables
strawberries = m.addVar(name="strawberries", lb=0)
apple_pies = m.addVar(name="apple_pies", lb=0)
apples = m.addVar(name="apples", lb=0)
peanutbutter_sandwiches = m.addVar(name="peanutbutter_sandwiches", lb=0)

# Define the objective function
m.setObjective(5 * strawberries + apple_pies + 2 * apples + 7 * peanutbutter_sandwiches, gurobi.GRB.MINIMIZE)

# Add constraints
m.addConstr(7 * strawberries + 7 * peanutbutter_sandwiches >= 94)
m.addConstr(18 * apples + 7 * peanutbutter_sandwiches >= 43)
m.addConstr(7 * strawberries + 7 * apple_pies + 18 * apples >= 53)
m.addConstr(7 * strawberries + 7 * apple_pies + 18 * apples + 7 * peanutbutter_sandwiches >= 53)
m.addConstr(35 * apple_pies + 12 * apples >= 28)
m.addConstr(35 * apple_pies + 23 * peanutbutter_sandwiches >= 16)
m.addConstr(12 * apples + 23 * peanutbutter_sandwiches >= 28)
m.addConstr(18 * strawberries + 23 * peanutbutter_sandwiches >= 31)
m.addConstr(18 * strawberries + 12 * apples >= 38)
m.addConstr(35 * apple_pies + 12 * apples + 23 * peanutbutter_sandwiches >= 35)
m.addConstr(18 * strawberries + 35 * apple_pies + 12 * apples >= 35)
m.addConstr(18 * strawberries + 35 * apple_pies + 23 * peanutbutter_sandwiches >= 35)
m.addConstr(35 * apple_pies + 12 * apples + 23 * peanutbutter_sandwiches >= 26)
m.addConstr(18 * strawberries + 35 * apple_pies + 12 * apples >= 26)
m.addConstr(18 * strawberries + 35 * apple_pies + 23 * peanutbutter_sandwiches >= 26)
m.addConstr(18 * strawberries + 12 * apples + 23 * peanutbutter_sandwiches >= 26)
m.addConstr(35 * apple_pies + 12 * apples + 23 * peanutbutter_sandwiches >= 23)
m.addConstr(18 * strawberries + 35 * apple_pies + 12 * apples >= 23)
m.addConstr(18 * strawberries + 35 * apple_pies + 23 * peanutbutter_sandwiches >= 23)
m.addConstr(-3 * strawberries + 2 * apple_pies >= 0)
m.addConstr(-apple_pies + 2 * peanutbutter_sandwiches >= 0)
m.addConstr(18 * apples + 7 * peanutbutter_sandwiches <= 113)
m.addConstr(7 * strawberries + 18 * apples <= 144)
m.addConstr(7 * strawberries + 18 * apples + 7 * peanutbutter_sandwiches <= 192)
m.addConstr(7 * apple_pies + 18 * apples + 7 * peanutbutter_sandwiches <= 311)
m.addConstr(7 * strawberries + 7 * apple_pies + 18 * apples <= 186)
m.addConstr(18 * strawberries + 12 * apples <= 88)

# Optimize the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", m.objval)
    print("Strawberries: ", strawberries.varValue)
    print("Apple Pies: ", apple_pies.varValue)
    print("Apples: ", apples.varValue)
    print("Peanutbutter Sandwiches: ", peanutbutter_sandwiches.varValue)
else:
    print("The model is infeasible")
```

## Step 6: Provide the symbolic representation in JSON format
```json
{
    "sym_variables": [
        ["x0", "strawberries"],
        ["x1", "apple pies"],
        ["x2", "apples"],
        ["x3", "peanutbutter sandwiches"]
    ],
    "objective_function": "5*x0 + x1 + 2*x2 + 7*x3",
    "constraints": [
        "7*x0 + 7*x3 >= 94",
        "18*x2 + 7*x3 >= 43",
        "7*x0 + 7*x1 + 18*x2 >= 53",
        "7*x0 + 7*x1 + 18*x2 + 7*x3 >= 53",
        "35*x1 + 12*x2 >= 28",
        "35*x1 + 23*x3 >= 16",
        "12*x2 + 23*x3 >= 28",
        "18*x0 + 23*x3 >= 31",
        "18*x0 + 12*x2 >= 38",
        "35*x1 + 12*x2 + 23*x3 >= 35",
        "18*x0 + 35*x1 + 12*x2 >= 35",
        "18*x0 + 35*x1 + 23*x3 >= 35",
        "35*x1 + 12*x2 + 23*x3 >= 26",
        "18*x0 + 35*x1 + 12*x2 >= 26",
        "18*x0 + 35*x1 + 23*x3 >= 26",
        "18*x0 + 12*x2 + 23*x3 >= 26",
        "35*x1 + 12*x2 + 23*x3 >= 23",
        "18*x0 + 35*x1 + 12*x2 >= 23",
        "18*x0 + 35*x1 + 23*x3 >= 23",
        "-3*x0 + 2*x1 >= 0",
        "-x1 + 2*x3 >= 0",
        "18*x2 + 7*x3 <= 113",
        "7*x0 + 18*x2 <= 144",
        "7*x0 + 18*x2 + 7*x3 <= 192",
        "7*x1 + 18*x2 + 7*x3 <= 311",
        "7*x0 + 7*x1 + 18*x2 <= 186",
        "18*x0 + 12*x2 <= 88"
    ]
}
```