A firm produces output according to the production function:

Q=F(K,L)= 4K + 8L

a. How much output is produced when K=2 and L=3?

32 units

b. If the wage rate is $60 per hour and the rental rate on capital is $20 per hour, what is the cost minimizing input mix for producing 32 units of outputs?

capital:

labor:

c. If the wage wage rate decreases to $20 per hour but the rental rate on capital remains at $20 per hour, what is the cost-minimizing input mix for producing 32 units of output?

capital:

labor:

I have read and re-read the corresponding chapter, and I am just not understanding! I figured out a, but I am stuck on the other two. I would like step-by-step answers with explanation in hopes it will help me understand the rest of the chapter.