If we simply divide the volumes we get 9*10*14/(1*3*4)=1260/12=105. But to do this we would need to split some blocks. However, we know the answer cannot be bigger than 105. The 1" side of a block will fit exactly any side of the prism, so we can reduce the problem to filling an area measuring 9*10, 9*14 or 10*14 with 3*4. 6 of these blocks would exactly fill an area A 9*8, 9 would fill area B 9*12, and 8 would fill area C 8*12. For area A there would be a stack of 14 blocks making 84 blocks in all; area B a stack of 90; area C a stack of 72.
Now we look at wastage. How many blocks can we use to fill the gaps for area B? What we have left measures 2*10*9. We can consider areas again because we can only arrange the blocks two blocks deep to make up 2 inches. So the area we have to fill is 10 by 9. We need 6 blocks to fill 8 by 9, and, because there are two layers we can use up 12 blocks. That means in all we use 90+12=102 blocks out of a maximum of 105. The volume remaining is 36 cu in. The 12 blocks are arranged 2 blocks deep by 2 blocks wide (2*4") by 3 blocks long (3*3"), leaving a gap, measuring 2*2*9 into which no more blocks will fit.