to open up a small daily supply of Kernite in Highsec, here is how this can be done.

• a toon that NOT yet has completed the Carrer mission arc. (can be a alpha clone)
• 0 ISK needed
• no skills required
• no ship needed

Short Version:

• go to a School system like Clellinon
• board a Corvette
• speak to the Career Agent Industrialst – Producer
• complete the missions Making Mountains of Molehills up to mission 8 of 10 in the Corevette.
• on Mission 4, you have to kill the rats even if you have prepared the Tritanium.
  you can skip the assembly of the Venture, if you plan on using it, assemble & board then just strip the Corvette and trash it, so you can use the civilian gun on the Venture for free.
• complete all missions until Mission 8 of 10 is completed.
• start mission 9 (this is the mission we want to “keep”)
  
  the goal here is NOT to deliver the “Production assistant”
• Warp to the site & approach the Kernite asteroids
• press [CTRL]+[B] to bookmark the location
• do NOT Kill the Rat called Coreli Initiate
  (you can kill other Rat’s if they anoy you too much)
  as you can see, it applies very little damage, there is little to no risk by letting it just shoot you.
  
  (just orbit the asteroid and let them shoot at you.
• do NOT mine all asteroids, leave the smallest rock behind.
• with the rat still active, and some ore left, on the server reset at 11:00 the whole field will be restored.

after 11:00 warp to the bookmarked location and repeat, mine all but one asteroid, and NOT Kill Coreli Initiate.

doing this gives you around 6000 m3 of Kernite (5.7 Million ISK*)

which is not that much, but since those missions do stay alive, you can just do this with multiple accounts, and just use a larger ship and fly from bookmark to bookmark.

To Speedrun the Missions, bring with you
– 1 1MN Civilian Afterburner
– 7000 Tritanium (you still need to go out on mission 4 to kill the rats)
– 20 Cap Booster 25
(it all fits in a Corvette (exept the amarr one))