A year ago, a major potato producer suffered serious losses when a virus affected the crop at the company's North Holt farm. Since then, steps have been taken to eradicate the virus from the soil, and the specialist who directed these operations estimates on the basis of the preliminary evidence, that there is a 70% chance that the eradication program has been successful. The manager of the farm now has to decide on his policy for the coming season, and he has identified two options: 1. He could go ahead and plant a full crop of potatoes. If the virus is still present, an estimated net loss of $20,000 will be incurred. However, if the virus is absent, an estimated net return of $90,000 will be earned. 2. He could avoid planting potatoes at all and turn the entire land over to the alternative crop. This would lead to net returns of $30,000 with certainty. Later, the manager is informed that a laboratory could carry out a test on the farm that will indicate whether or not the virus is still present in the soil. The manager has no idea as to how accurate the indication will be or the fee that SU Labs will charge. a) What is the upper bound on the amount that the manager would pay to the laboratory? b) Suppose that after making further enquiries, the farm manager discovers that the laboratory test is not perfectly reliable. If the virus is still present in the soil the test has only a 90% chance of detecting it, while if the virus has been eliminated there is a 20% chance that the test will incorrectly indicate its presence. How much would now be worth paying for the test?