Hello! I am having a really tough time starting this problem on short-run cost functions. I've attempted to use the short-run (total) cost function of STC but can't seem to understand how to solve it because we aren't given the value of our fixed value K.

I am given the following firm with a long-run production function Q=f(L,K)= LK where Q is output, L is labor input and K is capital input. Input prices are w=4 and r=9 per unit of labor and capital, respectively. Suppose, capital is fixed at level K = K-bar in the short run.

1) What is the firm's total cost function in the short-run?

2) Marginal cost in the short run?

3) Average cost in the short run?

4) For Q*>), in the long-run, what is the firm's best 'plant size', K*(Q*), to produce output level Q* i.e. which K* minimizes the short-run total cost of producing Q*? (assuming input prices are still fixed at (w,r) = (4,9)