1. (25 points) A grocery store is considering the purchase of a standby power generation system to operate during times of power-outs of the main electric power grid (like the ones that happened in 2019 Fall due to wildfires). A manufacturer of a power generation system offers two types of financing: a. A down payment of $3,000 and an annual payment of $1,000 for 12 years. b. An annual payment of $1,300 for 12 years with no down payment. If the interest rate for financing is 8%, which of the two financing schemes is more economical based on present value criterion? Show your formulae and calculations. 2. (25 points) For the grocery store mentioned in problem 1, if the main electric power grid has a mean time between failures (MTBF) of 1,000 hrs., a. calculate the probability of uninterrupted power supply for 1,000 hrs. b. if the standby system has the same reliability as the main power grid, by how much does the probability of uninterrupted power supply increase? C. Draw a simple network configuration diagram showing the main power supply and the standby power supply. 3. (50 points) The grocery store offers online ordering of all its items through a website that is always on. The website has a MTBF of 200 hrs. It typically takes an average of 4 hrs. to bring the website back to operation after a failure. a. What is the failure rate for the website? b. If the website requires scheduled maintenance of five hours per week, what is the Active Maintenance Time? C. If the combined logistics and administrative delay times is 2 hrs. per maintenance, what is the mean downtime for the website? d. Calculate Inherent Availability for the website. e. Calculate Achieved Availability for the website. f. Calculate Operational Availability for the website