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:

Cost per gallon: Premium $0.32

Regular $0.30

Cost of checking the valve $80.00

Cost of adjusting the valve $40.00

Subjective estimates of the probabilities of the valves condition are estimated to be:

Event Probability

Valve in adjustment 0.7

Valve out of adjustment 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.