Suppose you are given the following equation for production function:

Q=21L + 9L^2 - L^3

where Q is the quantity of output and L is the quantity of labour input.

a)Sketch the production function and on a separate diagram sketch the MPL & APL curves. Indicate all the key values.

b) now suppose that the price of each unit of labour is $500, what is the TVC AND AVC when the firm maximises its labour productivity ?

c) on 3rd diagram, sketch the MC and and the AVC that correspond to the MPL and APL curves.

I need help with the graphs by clearly mentioning the points on the graph wherever required.

Thanks.