You are a risk manager for a manufacturing company, and you are evaluating the risk associated with a new production line. The production line has a fixed cost of $500,000 and a variable cost of $50 per unit. The selling price of each unit is $100, and the demand for the product follows a normal distribution with a mean of 10,000 units and a standard deviation of 1,000 units. You estimate that there is a 20% chance that demand will be less than 8,000 units. You decide to hedge the risk by purchasing a put option on the price of the product, which will protect the company from a decrease in the selling price. The strike price of the put option is $90, and the premium is $5 per unit. Assume that the number of units produced and the selling price are independent and identically distributed random variables.

(a) Calculate the expected profit of the production line without hedging.
(b) Calculate the expected profit of the production line with hedging.