I'll go with
As @justforplaylists suggest,
You can assume they have a certain base rate and a certain overtime rate, and that's why it costs more to do it in 5 months instead of 6.
double the first example and compare to the third
So it looks like
there is no overtime to do it in 6 months: rather, in the first example, they are slacking off and charging you. Bastards.
scaling up the third example, 15 men could build 5 houses in 6 months for \$100k, but, if you give them 8 months, they'll overcharge by \$25k.
In more detail:
According to OP, for \$50k, you get 2 houses in 6 months using 8 men. So you'd think that, if nothing else, you hire two entirely separate groups of 8 men, to act completely independently, and pay each group \$50k, and each group makes 2 houses in 6 months. Right? For \$100k, you get 4 houses in 6 months using 16 men.
But according to OP, for \$80k, you get 4 houses in 6 months using 12 men. So it seems that dding extra men is increasing the cost by \$5k for each man, for nothing.
Therefore they charge \$5k for 6 man months (no overtime), at it takes at most 18 man-months to build a house. The base cost of a house is therefore \$5k, plus \$15k labour.
You can work out how much overtime costs to get it done in 5 months (looks like the rush rate is really steep compared to the base rate - like twelve times), but it doesn't matter, because the question is for 8 months, there will be no overtime.
So, for 15 men to build 5 houses in 6 months would cost \$100k.
So it follows that for 15 men to build 5 houses in 8 months would cost
But we've already established that
if you give them more man-months than necessary, these guys will happily just charge you more for nothing. So in this case they're going to overcharge you 30 man months. 6 man months costs \$5k, so 30 costs \$25k
For a total of