Hi please use the given information to answer each part of the problem and please include a short explanation, drawing, or steps/formulas to improve my understanding of the problem. Thank you!

Power, Ltd. has been contracted to construct a new power plant, and they have tapped you to do a cursory economic analysis to help narrow down the designs. They want to be able to deliver low-cost power to their customers. Design 1 is a coal power plant with a nameplate capacity of 500 MW, and an expected capacity factor of 40.2%. The overall efficiency of the plant is expected to be 33%. The capital cost is $1,500/kW, and the yearly non-fuel O&M cost is $30/MWh. Design 2 is a combined cycle gas power plant with a nameplate capacity of 500 MW, and an expected capacity factor of 56.6%. The overall efficiency of the plant is expected to be 55%. The capital cost is $1000/kW and the yearly non-fuel O&M cost is $27.74/KW. UE power has a gas delivery contract at $3/MMBtu and a coal delivery contract at $1/MMBtu for the next 20 years. You are to calculate the LCOE assuming a 20-year lifetime, and a discount rate of 8%. a) What is the total annual generation for each plant in MWh? b) How much coal will design 1 use and how much gas will Design 2 use? (answer in MMBtu/yr and dollars/yr) c) What is the total annual O&M + fuel cost for each design ($/yr)? d) What is the capital cost ($) for each power plant? e) What is the annualized capital cost ($/year) for each power plant? f) What is the Levelized Cost of Energy for each power plant ($/MWh)