You are in charge of fuel price risk management for a major airline. There are no jet fuel options, so you use crude oil prices to represent jet fuel prices. The spot price for crude oil is $50.58 per barrel, the forward price for crude oil 6 months from now (August 2020) is $52.13, the premium for an August 2020 $52 call option is $4.24, and the premium for an August 2020 $52 put option is $4.51. Use an option to hedge the airline’s August 2020 oil purchases; assume an interest rate for 6 months (February to August) of 3% (i. e., 6% simple interest). Ignore commissions, margins, and other transaction costs. ) Show the profit table for the hedged position (crude oil + option) over a range of market prices for crude oil from $42 to $62 in $1 increments, and then answer these questions:

Is your position in jet fuel (represented here by crude oil) long or short? Why? [Hint: Are you at risk from higher oil prices, or lower oil prices?]
What is the maximum profit (per barrel) for the hedged position (crude oil + option) over this range of prices?
At what market price(s) does this occur? 
What is the maximum loss (per barrel) for the hedged position (crude oil + option) over this range of prices? At what market price(s) does this occur?