The ACME-Generation Company has a combined cycle plant with a capacity of 500 MW. The Directorate of Operations is planning the natural gas budget for the month of November 2023. It is estimated that the plant will need a batch of 2150.0 million cubic feet of natural gas to operate during that month. To ensure the price of the gas batch, the company acquires a call purchase option, European type. The bank with which it is negotiating offers the option at 5.0 US$/1000 ft3 with a premium of 0.2 US$/1000 ft3.

For this case: calculate the cost of the premium, and graph the benefit, expressed in US$/1000 ft3, based on the price of the underlying, which is natural gas. In particular, calculate the benefit when the price of gas is $3.5/1,000 ft3, or $7.0/1,000 ft3. Explain the payments that the company would make when the gas has the prices mentioned above.

Note: Consider that a cubic foot of natural gas has a heating value of 1030 Btu, when it is at a temperature of 60 F and with a pressure of 1 atm.