A drilling company produces oil. The profit function for the company is as follows:

Profit = ($100 - variable cost) X number of barrels sold - fixed cost

The current production rate is 5 million barrels per year. The firm can expand the production by conducting further stepwise exploration, adding 1 million or 2 million barrels per year with the following cost implications.

Scenarios	Capacity (barrel/year)	Fixed cost	Variable cost
Current	5 million	$10 million	$30 /barrel
Add 1 million	6 million	$14 million	$26 /barrel
Add 2 million	7 million	$18 million	$24 /barrel

Annual demand of oil is probabilistic with following distribution

Oil demand	Probability
3 million	0.1
4 million	0.2
5 million	0.3
6 million	0.3
7 million	0.4
8 million	0.4
9 million	0.2
10 million	0.1

Using Monte Carlo simulation (an Excel spreadsheet would be acceptable for this), develop a profit model for each of the 3 scenarios, and determine the average profit for each of the 3 scenarios. Use only 100 samples for your Monte Carlo simulation. Based on the results of your profit model, what would you recommend that this company do and why? Hint: Start by normalizing the given probabilities so they sum to 1.0.