Lots of a complicated machine part are obtained from a manufacturer. They may be tested only by actually using a sample of a few pieces. Suppose that it is known that the parts are produced by a process which turns out either 10% defectives or 4% defectives. Suppose further that it is agreed with the manufacturer that a sample of two parts may be taken from every lot for test checking. The cost of testing is Rs 2,000, the cost of accepting a defective part Rs 20,000 while the cost of rejecting a non-defective part Rs 2,000. Each lot consists of 50 parts and it is assumed that the 10% or 4% defective lots have 3:2 chances of occurrence. a) Draw an appropriate decision tree. b)State the optimal course of action for the firm indicating whether it is worthwhile to take a sample or not. c)Determine the cost of sampling that will make the firm in question neutral between taking and not taking a sample. d) Calculate the expected value of perfect information.