A price-taking firm's variable cost function is

VC=3Q^3

where Q is its output per week. It has a sunk fixed cost of $1,296 per week. Its marginal cost is

MC=9Q^2

a. What is the firm's supply function when the $1,296 fixed cost is sunk?

Q = (P/9)^0.5 for P $(answer here)

b. What is the firm's supply function when the fixed cost is avoidable?

Q = (P/9)^0.5 for P $(answer here)