A refinery has the crack spread of 5-3-2: 5 barrels of oil yield 3 barrels of gasoline and 2 barrels of heatingoil. The refinery buys crude at $52/bbl, spends $8/bbl for refining operations and sells gasoline and heatingoil at prices ofRg/bbl andRh/bbl respectively. Each price can take only two values:Rg {60, 66}andRh{62, 70}.a) What is the expected value of the refinerys profit from a barrel of crude oil if two values of each price arelikely to occur with equal probabilities and independent of the other price.b) Because of positive price correlation, low (high) gasoline price is coupled with low (high) heating oil price,so either both refined products assume low prices or both assume high prices. Hence, there are two scenariosonly: high refined product prices of(Rg,Rh) = (66, 70)or low refined product prices of(Rg,Rh) = (60, 62).If the two scenarios are likely to happen with equal probabilities, what is the expected value of the refinerysprofit from a barrel of crude?c) Review your answers to a) and b). Do you expect them to be different or the same, why?