Hi, I would really appreciate if you could help me understand how to solve this problem step by step. Thank you in advance.

1. Bong-Bong produces orange juice concentrate that operates in the competitive market. The estimated number of firms is 100.Suppose that the manager of the firm operating in a competitive market has estimated the firm's average variable cost function to be AVC=10-0.03q+0.00005q^2 and the total fixed cost is $600.

a)What is the corresponding marginal cost function?

b)At what output is AVC at its minimum?

c)What is the minimum value for AVC?

d)What is the shut-down price for this company?

e)If the forecasted price of the firm's output in $10 per unit, what is the optimal output and firm's profit? What is the producer surplus?

f)What would happen in the long run in terms of the number of firms, market price, and supply?

g)If there are 100 firms in the market producing Orange Juice concentrate, what is the total market supply and market producer surplus?