a) Discuss the various roles of quantitative techniques in business and (5 marks) Industry b) A company receives shipment of certain items. It should decide whether to accept or reject the shipment, on the basis of inspection of a sample selected from the shipment. From the past experience, it is known that the percentage of defective items in a batch of shipment is 0, 2 or 5, the probabilities for which are 0.5, 0.3 and 0.2 respectively. The company can accept only those batches which have no defectives. The cost of rejecting a good batch i.e. a batch with no defectives is $ 200. The cost of accepting a batch with 2 percent defective is $ 400 and the cost of accepting the batch with 5% defective is $ 600. A sample of 10 items has been selected from the shipment and two items are found to be defective. The conditional probabilities of getting 2 defectives in a sample of 10 items from the batch of 0%,2% and 5% defectives are calculated as 0.083, 0.185 and 0.265 respectively. Required: Determine whether the shipment should be accepted (10 marks) (6 marks) c) Discuss the steps involved in decision making in general. d) Using examples explain the criteria used in selecting an alternative in decision making. (4 marks)