Costs of Investigation: Texas Oil Company currently sells three grades of gasoline: regular, unleaded, and unleaded plus, which is a mixture of unleaded and an octane enhancer. Unleaded plus is advertised as being "at least 10 percent higher octane than unleaded." Although any mixture containing 10 percent or more premium gas could be sold as unleaded plus, it is less costly to increase the octane by exactly 10 percent. The amount of octane enhancer in the mixture is determined by a valve in the blending machine. If the valve is properly adjusted, the machine provides a mixture that yields the 10 percent higher octane. If the valve is out of adjustment, the machine provides a mixture that yields 20 percent higher octane. Once the machine is started, it must continue until 100,000 gallons of unleaded plus have been mixed.

The octane enhancer costs 5 cents per gallon to make unleaded plus at 10 percent higher octane than unleaded. If the 20 percent higher octane is produced, the octane enhancer costs 12'/4 cents per gallon. The probabilities of the valve's condition are estimated to be:

Required:

a. Should Texas investigate the valve?

b. At what probability would Texas be indifferent about whether to investigate?\

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Cost data available: Cost per gallon-unleaded Cost per gallon-regular Cost of checking the valve Cost of adjusting the valve 70 65 $1,000 $ 500