A boat manuf wants to know how many brakes to install. The brakes are independent in function and work with a probability of .8. They work in parallel so if one brake works the boat will be safe. If they all fail the boat will sink. If the boat sinks, the owner of the boat will sue and the cost of the lawsuit will be $1,000,000 for each lawsuit. Each brake costs $100 to install. The boat costs $5000 to build. The manuf will sell T boats at $10,000 each no matter how many brakes are installed, and the manuf wants to maximize profits.
a. how many brakes will be installed in each boat
b. given the number of brakes installed, what is the variance
c. what is the expectation of profits
d. if T = 40, what is the probability of a fatality given the number of brakes