Travis K. answered 09/07/22
Economics Tutor for MBA, Intro (Principles), AP Micro / Macro classes
The direct answer to your question is that the marginal rate of technical substution is:
MRTS = -Change in capital input/change in labor input
Often it's written as
-ΔK/ΔL
For example, if you have a production function like:
q = L1/4K3/4
Then the MRTS is:
-3/4K-1/4 / -1/4L-3/4
Which simplifies to:
3L3/4 / K1/4
As far as the rest of your statement goes. There are wonderful work-as-you-go courses online you can do for no cost or you can enroll in an intermediate microeconomics course. This type of problem is not a basic, principles of microeconomics topic.