Question 1 A food company runs a computerized processing plant and needs to formulate a series of decision rules to advise its managers on how they should react if the control panel indicates particular problems with the system. Because there is always a possibility that an indicated problem is in fact caused by a fault in the control panel itself, there is some concern that unnecessary losses will be incurred it production is halted because of a nonexistent problem. Light number 131 will illuminate on the panel if the computer detects that packs of a frozen food are being filled to below the legal weight. However, it is known that there is a 0.15 probability that this light will give a false alarm. In the event of this light illuminating , the manager would have to decide whether or not to gather further information before making a decision on whether to stop production immediately. Any stoppage would cost an estimated $150 000, but a decision to ignore the light would lead to losses of $300 000 it the bags being lled on the automatic production line really were underweight . If the manager decides to gather further information before taking the decision on whether to stop production then this will involve taking a sample from output and weighing the selected packs. This will render the sampled packs unsaleable and cost the company $5000. The sample will indicate whether or not there is a fault in production . but there is a 0.2 probability that it will give misleading results. Despite this it has always been company policy to take a sample because of the small cost of sampling relative to the other costs. (a) If the company's objective is to minimize expected costs. formulate a decision rule which will tell the duty manager how to react when light 131 illuminates. (b) Explain the rationale behind your recommended decision rule in non-technical terms. (c) Explain the role which sensitivity analysis could have in this