Please assist with these questions.

Estimate of the demand:

Q = 20000 + -100P + 0.50M + -300Pr

Average variable cost function:

AVC = 20 + -1.20Q + 0.03Q^2

Assume that M = $40,000, Pr = $4, and Fixed Costs = $8,000.

1. What is the firm's inverse demand function?
2. What is the firm's marginal revenue function?
3. What is the firm's estimated marginal cost function?
4. What is the firm's optimal level of production (how many units of the product should they produce)?
5. What is the firm's optimal price?
6. Should Tay's Technology shut down in the short run? Why or why not?
7. What is Tay's expected profit?