You plan to invest $4 million in the construction of an oil field that has a potential yearly revenue of $10 million. The oil well will be located in The Gulf of Mexico. As we all know, this region is constantly hit by hurricanes. Assuming that if during an entire year there is a hurricane, this will disrupt your production and your oil field will lose 20% of its yearly production. And if during a year there are two hurricanes, your field will lose 40% of its yearly production, if there are three hurricanes your field will lose 60% of its yearly production, if there are four hurricanes your field will lose 80% and if there are five or more hurricanes your field will lose its entire yearly production. According to the weather prediction, the yearly number of hurricanes that will hit this region follows a Binomial random variable with parameters n=5 and p=1/3. In order to reduce the risk of your investment, you plan to buy an insurance policy. One unit of this policy costs $1 and will pay $2 each time the region is hit by a hurricane. We know the expected rate of return as a function of the number of units insurance bought is (8,000,000 +7u)/(12,000,000+3u) and the expected total amount received as a number of units o insurance bought is 10(2,000,000+u)/3. What is the number of units that will minimize the variance?