Problem 5 (15 pts +10 pts extra points) The Royal Canadian Air Force is considering buying a new weapon system to use on its fighter aircraft for close-in air to air attack/defense after longer-range missiles have been expended. The existing Status Quo is the M61 20-mm gun, which are installed in the current aircraft but will need to be refurbished at a cost of $50 million. There are two additional alternatives: internallymounted twin 30mm guns and a new high-tech laser system. There are three evaluation measures that the Air Force will use for this decision: cost of implementing across the fleet (\$millions), capability, and survivability. The last two measures are constructive measures defined as follows: (specitic values are defined for these categories in measurable terms) For the following analysis, assume a range from $50M to $250M($M=$ million ) for cost across the service and a range from 1 to +2 for the (constructed) evaluation measure scale capability and from 1 to +1 for survivability. Note that preferences are monotonically increasing for capability and survivability ("more is better"), while preferences are monotonically decreasing for cost ("more is worse"). The scores for each of the three alternatives on these three evaluation measures are as follows: A multi-objective utility analysis is being done to evaluate these alternatives. The single dimensional utility function over cost is (normalized) exponential with an R value of $65M. The single dimensional utility function over capability is piecewise linear. The utility increment going from a capability score of 1 to a score of 0 is the same as the utility increment going from a capability score of 0 to a score of +1. The utility increment going from a capability score of +1 to a score of +2 is twice as great as the utility increment going from a capability score of 0 to a score of 1 . The single dimensional utility function over survivability is linear from 1 to +1. The utility increment going from a capability score of 1 to a capability score of +2 is twice as great as the utility increment going from a cost per weapon system alternative of $250M to a cost of $50M, while the utility increment going from a survivability score of 1 to a survivability score of +1 is the same as the utility increment going from a capability of 1 to a capability score of +2. Questions: a. Compute the one-dimensional utility values for each alternative for each evaluation measure. ( 15pts) b. Determine the swing weights for all three evaluation measures. ( 5pts) c. Determine the utility values of the three alternatives, and find which alternative is