I have starved characters to death to make the necessary money but I can't even get close to 10k what do I do? Is there any other way to do the mission? 

I have to say, the first thousand was hard, but I'm already at over  5k with 16 days to go until my next payment.  

A few hints from my own pov (which is untainted by any guides, just based on my own play):

Do goblin dungeons.  You should probably try to have at least one tank character (Seraphs make amazing front line tanks if you can snag one with decent stats) and a mage (I recommend "Scholar" for the early game since this brings healing to the table).  If you have a fairy or an elf, you can get the "Druid" class which has a powerful crowd control attack that stays useful throughout the run.

Anyway, do your dungeons when you can.  Use daisy for prostitution as she's practically designed for that specific use.  I generally use my free slave from the beginning to cook meat soups and fish cakes (my master character is a halfkin cat, so he loves that).  Meat soups are great for two reasons:  1.  Almost everyone loves them, and 2.  You get three food for the price of two!

In order to get a bit ahead, I started purchasing ALL the meat and vegetables that the shop provides.  I convert it all to  meat soups, then sell the majority of them back.  I spend 5 gold to make 3 meat soups, which then sell for a total of 9 gold, almost doubling my money every time.    This adds up over time.

Make sure that you have room when you start going after bandits.  You can capture and sell the leaders at the end for a little bit of extra money on top of whatever else you get just from running the dungeon.  Usually around 2-300 gold for them.

If you have extra resources and a character who is good at it, use your forge to craft high powered items to sell back.  The resources and time are well worth the 300+ you'll get off of decent quality items.

I was always suffering from a lack of funds in the early days of my game, but after reading your article, my business start-up has become much more stable. thanks for the Topic

Its actually really easy, just need to know how the game works. You can have a mansion full of prostitutes and make the required money, you can also go the "fishing" method that people recommend here, but its even easier to use this "fishing" method to pay the first one, then before the second one sell fish to get enough money to buy the materials needed for the "Rough Wood" resource upgrade in the mansion (the store restocks each day). While passing days try to get worker outfits for each of your wood choppers as well as some axes and use the "Dates" to train their physic. More Physics = more wood. As they get exp give them any classes that give +Collection or Physic bonuses, and obviously when recruiting new people prioritize people with higher Physic. As it is right now I've just paid off the 2nd loan and have more than enough to pay off the third loan. By the time I hit the 3rd one I would have LONG since had enough for the 4th one.

The above is roughly the same for the 'prostitute' route just with a focus on charm instead. And if you want to go the fishing route, Wits is what you aim for. It'll show you what stat and item each job uses on the job assignment screen at the bottom. Just make sure you remember to sell the wood / fish before the loan day rolls around.