4. (approx. 20-30 minutes) Suppose that Xcel Energy owns the only natural gas pipes going into every home in a small town, so it is the only company that can sell natural gas. The more natural gas it wants to sell, the less it can charge its customers. The (monthly) demand for natural gas is given by the equation that describes consumers' willingness to pay (or demand), WTP $100 - $100 Meanwhile, Xcel Energy's costs are described the equation C = $20+ $100, because it costs $20 to connect the town to Xcel Energy's plant and $10 to provide technical support and maintenance for each home. Xcel Energy's costs are shown below as well as its Total Revenue, assuming it charges all customers the same rate. a. Complete the following table.; use the formulas discussed in class -- You do not need to use calculus. Quantity 0 1 2 3 4 5 6 Willingness To Pay 100 90 80 70 60 50 40 Total Cost $20 $30 $50 $80 Average Marginal Total Marginal Cost Cost Revenue Revenue $0 -- $30.00 $16.67 $14.00 $10 $10 $10 $10 $90 $160 $250 $90 $50 $30 -$10 Profit -$20 $60 $120 $160 6 $160 b. Identify the profit-maximizing level of output, its corresponding price level, and the associated profit level. What is the reason for your selection? c. Based on the WTP that is given here, write down the revenue function, marginal revenue function, and the average revenue function.