First, the initial, pre-inflation, cost of the project was 450 + 30 + 80 = $<<450+30+80=560>>560.
Then, the price of the lumber increased to 450*1.20 = $<<450*1.20=540>>540.
Similarly, the price of the nails increased to 30*1.10 = $<<30*1.10=33>>33.
And the price of the fabric increased to 80*1.05 = $<<80*1.05=84>>84.
Therefore, the new, post-inflation, cost of the project is 540 + 33 + 84 = $<<540+33+84=657>>657.
Thus, the cost has increased by 657 - 560 = $<<657-560=97>>97.
#### 97