Juanito Corporation operates a railroad, and the cost of its operations largely depends on the oil price. The company requires $100,000$ barrels of crude oil $($bbls$)$ to run its railroad and complete other operations. A barrel of crude oil currently costs $$78\mathrm{.}25$ in the market.

The company worries that the oil price will rise over the next year, and its costs may be higher than they can afford. Juanito decided to hedge their current short position $($the obligation to buy oil one year from now$)$ by purchasing call options on crude oil.

Juanito wants to fully hedge against the risk of a rising oil price to keep its costs from exceeding $$85/$bbl$.$ Crude Oil call options with an exercise price of $$85/$bbl currently cost a premium of $$3\mathrm{.}20$ per contract. Each contract is for $1,000$ bbls and expires in precisely one year.

$1.$ How many of these contracts should Juanito purchase to hedge their exposure fully?

$2.$ Should Juanito exercise its options if the crude oil price falls to $$75/$bbl by the end of next year? Explain.

$3.$ What is Juanito$$s total profit from their options in this case?

$4.$ Should Juanito exercise its options if the crude oil price rises to $$92\mathrm{.}40$ by the end of the next year? Explain

$5.$ What is Juanito$$s total payoff from exercising their options in this case?

$6.$ What is Juanito$$s total profit from exercising their options in this case?

$7.$ Draw the profit and payoff diagrams for one crude oil call option contract.

$8.$ What is the breakeven crude oil spot price for this call option? $($I$.$e$.,$ the point at which profit is precisely equal to zero$)$