Why are we comparing the ratios of MPL to price of labor and MPK to price of capital not ratios of MPL and MPK to price of labor and price of capital
You can do both. Effectively you say "let me move one dollar from labor to capital expenditure and see what happens". By doing so you have reduced labor by 0.01 and thus reduced production by 0.15 chairs, but increased capital by 0.02 and thus production by 0.2 chairs. Net effect is 0.05 chairs more at the same cost.

Equivalently, MPL/MPK = 1.5&lt; w/r =2, or MPL/w= 0.15 &lt; MPK/ r = 2. Second is just rearrangement of the first, but with both you answer where the dollar of you cost is more efficient.