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. Benefit Design Cost (3) 90 000 20 100 110 000 70 170 000 100 90 60 000 50 (a) 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, 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.' (b) 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 (e) The manager also decides that if he was offered a hypothetical design which had the lowest reliability and the worst environmental impact he would be prepared to pay $120 000 to convert that design to one which had the best impact on the environment but which still had the lowest level of reliability. Which design should the manager choose