You have 2 unknowns so you need to find 2 simultaneous equations and solve them.
There are 2 ways to do this, the long way and the short way.
The long way to do this is to set up a lagrangian. You want to minimise the total cost, subject to the constraint that you have produced 121000 airframes.
Total cost: K + 10L
If you solve this in the usual way, you will get 2 simultaneous equations:
Solve those to get your answers of L and K.
You only need the ratio L/K. You can get this from the second simultaneous equation on its own
Interestingly, for this production function, the ratio of K/L is constant at all levels of output. So you didn't need to know that there were 121000 airframes after all.