A recent engineering graduate from Chico State is assessing an energy efficient water distribution systems that will cost $600,000 more initially, but will reduce annual pumping costs. The optimistic, most likely, and pessimistic cost scenarios are evaluated, where annual savings could lead to $80,000, $50,000, and $7, 500 with probabilities of 25%, 45%, and 30%, respectively. Additionally, an interest rate of 5% or 6% is equally possible, where each interest rate has the same likelihood. The lifespan is known to be 50 years, Calculate the present worth and joint probability of each possible combination of annual savings and interest rate scenarios, what is the expected present worth? Briefly discuss your findings in relation to the scenarios evaluated