This is a helpful write-up by EVE Player Kjellerup:

When you produce stuff there is always some kind of waste involved. This waste can be decreased by two things:

1) Your Production Efficiency skill (Reduces incompetence waste). Called PE.
2) The Material Research Level of the BPO (Reduces design waste). Called ME.

Wasteage is always added to the base mineral amount of what you are producing, and no skill level or ME lvl can reduce mineral cost below the base amount. Base amount is best found by looking up the item in item database on the Eve website.

First let me point out that there's a little confusion as to incompetence waste. According to the skill Production Efficiency it reduces waste by 4% per skill level, but according to the formula in the Player Guide it reduces waste by 5% per skill level. In the following I will assume it's 25% minus 5% per skill level, but it doesn't really matter if it's so or 20% - 4% per skill level, as you definitely want this skill at lvl 5 when going into production.

On a note some people will probably come here saying it's 25% - 4% per lvl, meaning you will always have a 5% incompetence waste, even at PE lvl 5. This is not true, as it's been tested and the numbers ingame simply gives PE5 a 0% incompetence waste.

Your base incompetence waste is 25%. Therefore you can calculate a formula for incompentence waste as: 1.25 - 0.05 * PE lvl.

When you reach PE lvl 5 you are no longer incompetent at producing, so personally you have no waste. Unfortunately the BPO which you just bought have a few design flaws that gives it design waste. You can reduce this waste by researching the Material Level (ME) of the BPO. You can see the design waste on the BPO under Wasteage Factor. This is always 10% (0.1) except for some rare items that have a 5% (0.05) Wasteage Factor. Drones used to have a 5% wasteage factor, but apparently they don't anymore. By researching the BPO we can reduce the design waste using the following formula: 1 + Base Wasteage / (1 + ME lvl).

Let's do some numbers for ME then. Using the above formula on a BPO with 10% base wasteage, we can calculate our production waste (assuming PE 5) to be:

ME0 - 10%
ME1 - 5%
ME2 - 3.3%
ME3 - 2.5%
ME10 - 0.9%
ME50 - 0.2%

As you can see, ME lvl's from 1 - 10 takes wasteage from 10% to 1% whereas lvl's 11 - 50 only takes it from 1% to 0.2%. For some people this will mean that researching a BPO above ME10 is a waste of time as you're only removing the last 1% of waste on those levels. I will leave that decision up to you. Generally the bigger the item, the more it will gain from being researched above ME10 but then again bigger items have a tendency to take ages for just one ME lvl.

Let's take what we know now and see an example. I will use the Kestrel for this example. Looking at the Kestrel BPO we can see that it requires the following materials:

Tritanium - 14,852
Mexallon - 2579
Isogen - 861
Noxcium - 1
Zydrine - 1