Let the supply and demand functions for winter coats be given by: S = 200 + 15p and D = 1400 45p where S denotes the quantity supplied of coats, D denotes the quantity demanded of coats, and p denotes the price of coats. (a) Use Excel to produce a table listing the quantity demanded and quantity supplied for the following prices: p = 5, 10, 15, 20, 25, 30. (b) Use Excel to generate a plot of the market equilibrium. (c) Use algebra to find the equilibrium price and quantity (must show your work). (d) Explain what would happen to the equilibrium in the market for winter coats if the government set a price ceiling of 10. Be sure to quantify any resulting shortage or surplus using the provided supply and demand functions.