Pinder Ltd buys 392,380 barrels of crude oil each year to produce 307,812 barrels of refined oil products. Pinder Ltd has a price policy where Pinder Ltds refined oil products are priced at 200% of the crude oil price. Pinder Ltd has no problems selling all of its products as long as it keeps to that price policy. For example, if the price of crude oil is $18 per barrel, the price of Pinder Ltds refined oil products will be $36 per barrel. Last year, the price of crude oil was $40 per barrel, and all other costs for Pinder Ltd excluding the cost of purchasing crude oil, such as wages and maintenance costs, added up to a total of $1,000,000. The price for this years crude oil has yet to be determined, but Pinder Ltd expects crude oil prices to remain at $40 per barrel with 40% probability, fall to $30 per barrel with 30% probability, and rise to $50 per barrel with 30% probability. Additionally, the other costs (which was $1,000,000 last year) is expected to rise by 10% this year, regardless of crude oil prices. Pinder can go long on call or put options with the crude oil as the underlying asset and an exercise price of $40 that expire this year, when the profits for the firm are generated. The price of the call/put options are $0.11 per option, where one option gives the holder the right to buy/sell one barrel of crude oil. Pinder Ltd wants to take the smallest option position possible so that its net income for this year does not fall below $6,000,000. Assume that there are no taxes. Based only on the information above, which of the following option positions should Pinder Ltd take? (round to the nearest two decimal places)

Group of answer choices

a) Long 35,715.71 call options

b) None of the other answers.

c) Long 35,715.71 put options

d) Long 45,716.29 call options

e) Long 45,716.29 put options