Question: Question 4: A natural gas company wants to develop an optimal trading plan for the next 10 days. The following table summarizes the estimated prices (per thousand cubic feet – cf) at which the company can buy and sell natural gas during this time. The company may buy gas at the "Ask” price and sell gas at the “Bid” price

The company currently has 150.000 cf of gas in storage and has a maximum storage capacity of 500.000 cf. To maintain the required pressure in the gas transmission pipeline system, the company can inject no more than 200.000 cf into the storage facility each day and can extract no more than 180.000 cf per day. Assume extractions occur in the morning and injections occur in the evening. The company pays a storage fee of 0.5% of the market (Bid price) value of the average daily gas in the inventory. (The average daily inventory is computed as the average of each days' beginning and ending inventory.)

Formulate the problem as an LP to maximize the profit during this period, while satisfying the necessary constraints. You do not need to solve the problem.