Bilco Oil Company currently sells three grades of gasoline: regular, premium and "regular plus", which is a mixture of regular and premium. "Regular plus" is advertised as being "at least 50% premium". Although any mixture containing 50% or more premium gas could be sold as "regular plus", it is less costly to use exactly 50%. The percentage of premium gas in the mixture is determined by one small valve in the blending machine. If the valve is properly adjusted, the machine provides a mixture which is 50% premium and 50% regular. Assume that if the valve is out of adjustment the machine provides a mixture which is 60% premium and 40% regular. Once the machine is started it must continue until 100,000 gallons of "regular plus" have been mixed. Cost data available: $0.32 $0.30 $80.00 $40.00 Cost per gallon: Premium Regular Cost of checking the valve Cost of adjusting the valve Subjective estimates of the probabilities of the valve's condition are estimated to be: Event Valve in adjustment Valve out of adjustment Probability 0.7 0.3 a.) The expected cost of checking the valve and adjusting it if necessary would be: b.) The conditional cost of not checking the valve when it is out of adjustment would be: Hint for b.) - Calculate the cost of fuel when valve is working properly and compare to cost of fuel when valve is not working properly.