The supply of and the demand for carrots:

S: Quantity Supplied = -7.37 + 76.92 * Price (quantity is in ton and price is in $/ton)

D:Quantity Demanded = 554.43 - 65.35 * Price(quantity is in ton and price is in $/ton)

Can you please show mathematically and explain how you got your answers? Thank you

a.) What is the equilibrium quantity in the carrots market?

b.) What is the equilibrium price in the carrots market?

c.) What is the consumer surplus in the carrots market at equilibrium?

d.) What is the producer surplus in the carrots market?

e.) What is the social surplus in the carrots market?

f.) The regulator considers intervening in the market for carrots by imposing a limit on production of carrots at 250 tons. What will be the deadweight loss in the market?