What is wrong with my throttle script?

I am creating a Aviation Controller. I had it all working great the other night and I got on this morning and the whole project was deleted somehow so I tried remembering what I did and I can't seem to figure out what I am doing wrong this time. (I've probably been spending too much time working on this game that I am blind to many mistakes so while I take a break I was wondering if anyone can tell me the answer to what I am doing wrong.

I know the answer is simple and I am just going about this the wrong way, but here is the part of the script that I am having trouble with.

 using UnityEngine;
 using System.Collections;
 
 /// <summary>
 /// Just to show the part I am having problems with.
 /// This is only a demo of a part of my Aviation Controller.
 /// 
 /// On this part what I am trying to do is create a throttle to a plane.
 /// When the user is holding down the Up/Down Arrows, smoothly increase the "throttleLevel".
 /// 
 /// At every throttleLevel it will set the Forward force of my aircraft a little higher. 
 /// (I have it all set up to allow editing in the inspector and it all works just fine.)
 /// 
 /// I just can't seem to make the arrows work. I am getting the error,
 /// 
 /// error CS0266: Cannot implicitly convert type `float' to `int'. An explicit conversion exists (are you missing a cast?)
 /// 
 /// I tried puting,
 /// throttleLevel += (int)1 * Time.deltaTime;
 /// throttleLevel += (float)1 * Time.deltaTime;
 /// (int)throttleLevel += 1 * Time.deltaTime;
 /// (float)throttleLevel += 1 * Time.deltaTime;
 /// 
 /// adding the "1.f" and "1.0" and "1.0f" I mean I was trying everything even what didnt make sense.
 /// 
 /// and also switching the variable from int to float. not that I thought any of this would work, but like I said I am
 /// very very... tired.. 
 /// 
 /// </summary>
 
 public class NewBehaviourScript : MonoBehaviour {
 
     
     //---------Variables Start--------
     
     public int throttleLevel;
     
     //---------Variables End----------
     
     
     
     // Update is called once per frame
     void Update () 
     {
     
         //----Creating our throttle---
     
         switch (throttleLevel)
         {
             case 1:                    //If throttleLevel = 1, throttle = 1. 
                    throttle = 1;
             break;
             case 2:
                 throttle = 2;        //If throttleLevel = 2, throttle = 2 and so on...
             break;
             case 3:
                 throttle = 3;
             break;
             case 4:
                 throttle = 4;
             break;
             case 5:
                 throttle = 5;
             break;
             case 6:
                 throttle = 6;
             break;
             case 7:
                 throttle = 7;
             break;
             case 8:
                 throttle = 8;
             break;
             case 9:
                 throttle = 9;
             break;
             case 10: 
                 throttle = 10;
             break;
         }
         
         //If the up arrow is being held, add 1 per second.
         if(Input.GetAxis("Vertical") >0) 
         {
             throttleLevel += 1 * Time.deltaTime;
         }
         
         //If the down arrow is being held, take away 1 per second.
         if(Input.GetAxis("Vertical") <0) 
         {
             throttleLevel -= 1 * Time.deltaTime;
         }
         
         //Set the max throttle level to 10.
         if(throttleLevel >= 10)    
         {
             throttleLevel = 10;
         }
         
         //Prevent the throttle level from falling below 0.
         if(throttleLevel <= 0)    
         {
             throttleLevel = 0;
         }
         
         //---------End----------
     }
 }