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Case study A chemical company is expanding its operations and a disused woolen mill is to be converted into a processing plant. Four companies have submitted designs for the equipment which will be installed in the mill and a choice has to be made between them. The manager of the chemical company has identified three attributes which he considers to be important in the decision: cost,' 'environmental impact' and * reliability. He has assessed how well each design performs on each attribute by allocating values on a scale from 0 (the worst design) to 100 (the best). These values are shown below, together with the costs which will be incurred if a design is chosen. Data Design Cost ($) BENEFITS Environmental Reliability Impact 20 100 90000 110000 170000 60000 100 90 50 0 D Normalized weights 30 The manager is having difficulty in allocating weights to the two benefit attributes. Assuming that the two weights sum to 100 and that mutual preference independence exists between the attributes. Question 1. perform a sensitivity analysis to show how the design offering the highest value for aggregate benefits will vary depending upon the weight which has been allocated to 'environmental impact. Calculate the aggregate benefice regarding the environmental impact for the four designs. Question 2. Eventually, the manager decides to allocate 'environmental impact'a weight of 30 and reliability' a weight of 70. By plotting the benefits and costs of the designs on a graph, identify the designs which lie on the efficient frontier