Should I invest 50% of my savings (20K) into a family business?

Since you are not familiar with rice farming, you should ask your relative more questions and do some research to check if the numbers are reasonable.

You want to understand the business plan. In particular: What exactly is the 20K to be spent on? Whose land and labor are being used and how are they valued/compensated? What does your relative get out of the deal?

If you decide to proceed, make a written contract so the terms are clear.

No, you shouldn't. Reasons are:

• A 15% ROI in 4 months is likely either simply a wrong guess by your relative, willful deceit or attached with significant, unspoken of risk. This turns your investment into gambling. You should not gamble with 50% of your networth, even if you might be able to replace it comparably quickly with your current salary.
• Don't mix family and investments. What happens if you won't get the expected return? What if you don't get anything back? Will there be resentment? Will you sue (if you have a contract)? This might lead to uncomfortable family gatherings in the future and might force other members of your family to pick sides.
• You lack knowledge in the industry (and so does he if he is just starting this month). Don't invest in something you don't understand sufficiently. If the investment unexpectedly does work out well for you, you might mistakenly assume it's because of your skills rather than sheer luck, potentially leading to further bad decisions in the future.
• If it would be a great decision, the person should be able to acquire 20k on their own from a bank. If they cannot get 20k from a bank in the current environment, you should second guess their business acumen as reflected in their personal finances.

If you still decide to do it, do get a contract as pointed out by nanoman.

1. It's a complete, total, scam^†

2. If you truly want to try something like this, try a small amount. Based on your outstanding financial condition as described, you could try $1,000. If the system is so fantastic, you'll make money on that. ABSOLUTELY DO NOT PUT IN MORE THAN $1,000. IF THE MINIMUM IS HIGHER THAN THAT FORGET IT.

3. Here's what you say when someone wants $20,000 from you:

Jack, that's a fantastic idea. Let's do this. You grab your credit card, and buy $20,000 of the stuff. Let's review your results after the three months. The profit will easily cover your small interest charges on the card. Let's get started! I'm more than happy to help by driving the truck or whatever is needed. Once we've tested that it works a couple times with your credit card, I may invest too.

^† I have no idea "who" the scam is enacted by, it could be anyone up and down the line. Your Family Member who is suggesting the idea could well be being scammed.