1. **Problem Statement:** We need to model a vending machine as a finite state automaton (FSA) that accepts inputs of money denominations Rp. 5,000, Rp. 10,000, Rp. 20,000, and Rp. 50,000. 2. **Machine Rules:** - The user first selects an item priced at Rp. 10,000, Rp. 15,000, or Rp. 20,000. - Then the user inserts money. - The machine accepts only valid denominations and rejects any input below Rp. 100,000 total. - The machine gives change if the inserted money exceeds the item price. - No money is returned if the total inserted is exactly the item price. 3. **Finite State Automaton Construction:** - **States:** Represent the amount of money inserted so far. - **Start State:** After item selection, initial money inserted is Rp. 0. - **Transitions:** Labeled with valid money inputs (5,000; 10,000; 20,000; 50,000). - **Accept States:** When the total inserted money is at least the item price. - **Reject Transitions:** For invalid denominations or if total inserted is below Rp. 100,000. 4. **Example for item priced Rp. 15,000:** - Start at state $S_0$ (0 inserted). - Insert Rp. 5,000: move to $S_5$ (5,000 inserted). - Insert Rp. 10,000: move to $S_{15}$ (15,000 inserted), accept state. - Insert Rp. 20,000: move to $S_{25}$ (25,000 inserted), accept state with change $25,000 - 15,000 = 10,000$. 5. **Change Calculation:** $$\text{Change} = \text{Total Inserted} - \text{Item Price}$$ 6. **Rejecting Invalid Inputs:** - If input money is not in {5,000; 10,000; 20,000; 50,000}, reject. - If total inserted money is less than item price, remain in intermediate states. 7. **Summary:** The FSA has states representing cumulative money inserted, transitions for valid money inputs, and accept states when enough money is inserted to buy the selected item, with change given if overpaid. This model can be drawn as a directed graph with nodes labeled by cumulative money and edges labeled by inserted denominations.