I am not to sure what the error is in my code but the order variable does not seem to initialise properly and hence my gui displays the wrong output, for example when cheese,tomato and chicken are selected it only displays Chicken with Tomato Tomato $12.75. Any help will be greatly appreciated :)

// Provided file for Week 10 Lab - first exercise

import java.awt.*;
import java.awt.event.*;
import javax.swing.*;

class PizzaFrame extends JFrame 
{
    // The following components are defined (but not created).
    private JButton newButton, exitButton;
    private JLabel priceLabel, grandTotalLabel;
    private JCheckBox chkCheese, chkChicken, chkTomato;
    private JTextArea jTA;

    // Other values used throughout this frame
    private double total, orderTotal, grandTotal;
    private String order = "";
    private static final String noOrder =  "Base price of basic pizza is $10.00";

    // set up GUI
    public PizzaFrame() 
    {
        // Ensure there is a suitable title for the frame
        setTitle("Welcome to Mylo's Pizza world, please make an order");
        setLayout(new FlowLayout());

        // Create the buttons for the user to click, and add them to the frame
        newButton = new JButton("New Order");
        exitButton = new JButton("Exit \t \n");
        add(newButton);
        add(exitButton);

        // Create the Check Boxes and add these to the frame.
        chkCheese = new JCheckBox("Cheese");
        chkChicken = new JCheckBox("Chicken");
        chkTomato = new JCheckBox("Tomato");
        add(chkCheese);
        add(chkChicken);
        add(chkTomato);

        // Create the Label which displays feedback to the user. Initially it should say the basic price.
        priceLabel = new JLabel(noOrder);
        add(priceLabel);

        // Create the TextArea in which to display the progressive orders.
        jTA = new JTextArea(10,10);
        //JScrollPane scroller = new JScrollPane(jTA);
        //jTA.setLineWrap(true);
        //scroller.setVerticalScrollBarPolicy(ScrollPaneConstants.VERTICAL_SCROLLBAR_ALWAYS);
        //scroller.setVerticalScrollBarPolicy(ScrollPaneConstants.HORIZONTAL_SCROLLBAR_NEVER);
        add(jTA);
        //add(scroller);

        // Create the lower Label which displays the       
        grandTotalLabel = new JLabel("Startup - No orders taken yet. Total: $0");
        add(grandTotalLabel);

        // create and register an instance of inner class ButtonHandler to use for button event handling
        ButtonHandler event_handler = new ButtonHandler();
        newButton.addActionListener(event_handler);
        exitButton.addActionListener(event_handler);


        // create and register listeners for the JCheckBoxes
        CheckBoxHandler box_listener = new CheckBoxHandler();
        chkCheese.addItemListener(box_listener);
        chkChicken.addItemListener(box_listener);
        chkTomato.addItemListener(box_listener);

        //set the size of the frame
        setSize( 250, 310 );

    } 


    //---------------------------------------------------- inner class for button event handling
    private class ButtonHandler implements ActionListener 
    {
        // start new order or exit on button event
        public void actionPerformed( ActionEvent event ) 
        {
            orderTotal = total;
            grandTotal += orderTotal;
            //boolean action = false;
            if (event.getSource() == newButton) 
            {
                // TO BE COMPLETED
                order = "";
                chkCheese.setSelected (false);
                chkChicken.setSelected(false);
                chkTomato.setSelected(false);
                //String order_total = Double.toString(orderTotal);
                jTA.append(order + " $" + Double.toString(orderTotal) + "\n");



            }
            else if (event.getSource() == exitButton) 
            {
                System.exit(0);
            }
        } 
    } 


    //---------------------------------------------------- inner class for check box event handling
    private class CheckBoxHandler implements ItemListener 
    {
        static final double CHEESE_COST = 2.75;
        static final double CHICKEN_COST = 4.00;
        static final double TOMATO_COST = 0.50;

    // respond to checkbox events by adding cost of pizza topping options to price
        public void itemStateChanged( ItemEvent event )
        {
                total = 10.00;
                // TO BE COMPLETED
                //order = "";
                if (chkCheese.isSelected()) 
                    total = total + CHEESE_COST;
                else if (chkChicken.isSelected()) 
                    total = total + CHICKEN_COST;
                else if (chkTomato.isSelected()) 
                    total = total + TOMATO_COST;



                if (chkCheese.isSelected() && chkChicken.isSelected() && chkTomato.isSelected()) 
                {
                    order += "Cheese with Chicken and Tomato ";
                }
                else if(chkCheese.isSelected() && chkChicken.isSelected() && chkTomato.isSelected())
                {
                          //else
                              order += "Cheese with Chicken ";
                }
                else if(chkCheese.isSelected() && chkTomato.isSelected())
                {
                        //if (chkTomato.isSelected()) 
                            order += "Cheese with Tomato ";
                }

                else if (chkChicken.isSelected() && chkTomato.isSelected())
                {
                      //if (chkTomato.isSelected()) 
                          order += "Chicken with Tomato ";
                }
                else if(chkCheese.isSelected())
                {
                            order += "Cheese ";     
                }
                else if (chkChicken.isSelected())
                {
                          order += "Chicken ";
                }
                else if (chkTomato.isSelected())
                {
                          order += "Tomato ";
                }


            priceLabel.setText("Price of pizza is: $" +  Double.toString(total));
            grandTotalLabel.setText("Total income is: $" +  Double.toString(grandTotal));

        } 
    } 

    //----------------------------------------- Program Entry/Start point:

    public static void main( String args[] ) 
    {
        PizzaFrame pFrame = new PizzaFrame();
        pFrame.addWindowListener ( 

                                      // TO BE COMPLETED
                new WindowAdapter() 
                {   
                    public void windowClosing (WindowEvent e) 
                    {
                                System.exit(0); 
                    }            
                }   

        );                          

        // Show the pizza frame ...
        pFrame.setVisible( true );
    }
}

Try debugging the code by printing out the values that control what is added to the order variable.
Add lots of printlns statements.

When using if/else if statements the first one that is true will be the ONLY one that is executed.
Make sure the variables are tested in the correct order: Most conditions first, least last.

Perhaps you want to use nested if statements instead of having the same condition used so many times: if (chkCheese.isSelected() ...

a few issues: you are constantly adding to your order value, instead of overwriting it.
next problem, you are setting the prices for only one single ingredient. lose the else's in those statements.

two more problems: you are setting your checkboxes with .setSelected(false); those statements also trigger your listener.
so, set the text before you perform these setSelected(false) statements, and don't initialize your order variable to "" right before that.

just follow the below, I've added some print statements, so you can verify what I've said about those setSelected statements:

import java.awt.*;
import java.awt.event.*;
import javax.swing.*;
class PizzaFrame extends JFrame 
{
    // The following components are defined (but not created).
    private JButton newButton, exitButton;
    private JLabel priceLabel, grandTotalLabel;
    private JCheckBox chkCheese, chkChicken, chkTomato;
    private JTextArea jTA;
    // Other values used throughout this frame
    private double total, orderTotal, grandTotal;
    private String order = "";
    private static final String noOrder =  "Base price of basic pizza is $10.00";
    // set up GUI
    public PizzaFrame() 
    {
        // Ensure there is a suitable title for the frame
        setTitle("Welcome to Mylo's Pizza world, please make an order");
        setLayout(new FlowLayout());
        // Create the buttons for the user to click, and add them to the frame
        newButton = new JButton("New Order");
        exitButton = new JButton("Exit \t \n");
        add(newButton);
        add(exitButton);
        // Create the Check Boxes and add these to the frame.
        chkCheese = new JCheckBox("Cheese");
        chkChicken = new JCheckBox("Chicken");
        chkTomato = new JCheckBox("Tomato");
        add(chkCheese);
        add(chkChicken);
        add(chkTomato);
        // Create the Label which displays feedback to the user. Initially it should say the basic price.
        priceLabel = new JLabel(noOrder);
        add(priceLabel);
        // Create the TextArea in which to display the progressive orders.
        jTA = new JTextArea(10,10);
        //JScrollPane scroller = new JScrollPane(jTA);
        //jTA.setLineWrap(true);
        //scroller.setVerticalScrollBarPolicy(ScrollPaneConstants.VERTICAL_SCROLLBAR_ALWAYS);
        //scroller.setVerticalScrollBarPolicy(ScrollPaneConstants.HORIZONTAL_SCROLLBAR_NEVER);
        add(jTA);
        //add(scroller);
        // Create the lower Label which displays the       
        grandTotalLabel = new JLabel("Startup - No orders taken yet. Total: $0");
        add(grandTotalLabel);
        // create and register an instance of inner class ButtonHandler to use for button event handling
        ButtonHandler event_handler = new ButtonHandler();
        newButton.addActionListener(event_handler);
        exitButton.addActionListener(event_handler);
        // create and register listeners for the JCheckBoxes
        CheckBoxHandler box_listener = new CheckBoxHandler();
        chkCheese.addItemListener(box_listener);
        chkChicken.addItemListener(box_listener);
        chkTomato.addItemListener(box_listener);
        //set the size of the frame
        setSize( 250, 310 );
    } 
    //---------------------------------------------------- inner class for button event handling
    private class ButtonHandler implements ActionListener 
    {
        // start new order or exit on button event
        public void actionPerformed( ActionEvent event ) 
        {
            orderTotal = total;
            grandTotal += orderTotal;
            //boolean action = false;
            if (event.getSource() == newButton) 
            {
                // TO BE COMPLETED
           //     order = "";
                jTA.append(order + " $" + Double.toString(orderTotal) + "\n");
                chkCheese.setSelected (false);
                chkChicken.setSelected(false);
                chkTomato.setSelected(false);
                //String order_total = Double.toString(orderTotal);
            }
            else if (event.getSource() == exitButton) 
            {
                System.exit(0);
            }
        } 
    } 
    //---------------------------------------------------- inner class for check box event handling
    private class CheckBoxHandler implements ItemListener 
    {
        static final double CHEESE_COST = 2.75;
        static final double CHICKEN_COST = 4.00;
        static final double TOMATO_COST = 0.50;
    // respond to checkbox events by adding cost of pizza topping options to price
        public void itemStateChanged( ItemEvent event )
        {
                total = 10.00;
                // TO BE COMPLETED
                //order = "";
                if (chkCheese.isSelected()) 
                    total = total + CHEESE_COST;
                if (chkChicken.isSelected()) 
                    total = total + CHICKEN_COST;
                if (chkTomato.isSelected()) 
                    total = total + TOMATO_COST;
                if (chkCheese.isSelected() && chkChicken.isSelected() && chkTomato.isSelected()) 
                {
                    System.out.println("printed 1");
                    order = "Cheese with Chicken and Tomato ";
                }
                else if(chkCheese.isSelected() && chkChicken.isSelected() && chkTomato.isSelected())
                {
                    System.out.println("printed 2");
                              order= "Cheese with Chicken ";
                }
                else if(chkCheese.isSelected() && chkTomato.isSelected())
                {
                    System.out.println("printed 3");
                            order = "Cheese with Tomato ";
                }
                else if (chkChicken.isSelected() && chkTomato.isSelected())
                {
                    System.out.println("printed 4");
                          order = "Chicken with Tomato ";
                }
                else if(chkCheese.isSelected())
                {
                    System.out.println("printed 5");
                            order = "Cheese ";     
                }
                else if (chkChicken.isSelected())
                {
                    System.out.println("printed 6");
                          order = "Chicken ";
                }
                else if (chkTomato.isSelected())
                {
                    System.out.println("printed 7");
                          order = "Tomato ";
                }
            priceLabel.setText("Price of pizza is: $" +  Double.toString(total));
            grandTotalLabel.setText("Total income is: $" +  Double.toString(grandTotal));
        } 
    } 
    //----------------------------------------- Program Entry/Start point:
    public static void main( String args[] ) 
    {
        PizzaFrame pFrame = new PizzaFrame();
        pFrame.addWindowListener ( 
                                      // TO BE COMPLETED
                new WindowAdapter() 
                {   
                    public void windowClosing (WindowEvent e) 
                    {
                                System.exit(0); 
                    }            
                }   
        );                          
        // Show the pizza frame ...
        pFrame.setVisible( true );
    }
}
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