1 Vehicle purchase. A student living in Lower Hutt is considering the purchase of a new vehicle. An electric vehicle (EV) can be purchased for $40,000 and has a running cost of $0.20 per km. Alternatively, a (petrol) combustion vehicle (CV) can purchased for $25,000 and has a running cost of $0.45 per km. The student is determined to make a decision which minimises the total cost depending on the number of kilometres that the vehicle will be used. (Here you should assume that the running costs also account for periodic costs such as mainte- nance, insurance, registration.) (a) Describe the decision and environment variables associated with this problem. (b) Determine the utility function R(D, X) which maps the outcomes to the total cost incurred. (c) Use a break-even analysis to determine the number of km for which the optimal decision differs above and below this amount. Specifically, plot R(D, X), determine where the break-even point occurs and mark it clearly on your plot, then briefly describe the best decision either side of this point. (d) The student currently uses public transport at an estimated cost of $0.60 per km. If a decision to continue to use public transport is included in the problem, how does this change the optimal decision depending on the total distance travelled?
1 Vehicle purchase. A student living in Lower Hutt is considering the purchase of a new
vehicle. An electric vehicle (EV) can be purchased for $40,000 and has a running cost of $0.20
per km. Alternatively, a (petrol) combustion vehicle (CV) can purchased for $25,000 and has a
running cost of $0.45 per km. The student is determined to make a decision which minimises
the total cost depending on the number of kilometres that the vehicle will be used.
(Here you should assume that the running costs also account for periodic costs such as mainte-
nance, insurance, registration.)
(a) Describe the decision and environment variables associated with this problem.
(b) Determine the utility function R(D, X) which maps the outcomes to the total cost incurred.
(c) Use a break-even analysis to determine the number of km for which the optimal decision
differs above and below this amount. Specifically, plot R(D, X), determine where the
break-even point occurs and mark it clearly on your plot, then briefly describe the best
decision either side of this point.
(d) The student currently uses public transport at an estimated cost of $0.60 per km. If a
decision to continue to use public transport is included in the problem, how does this
change the optimal decision depending on the total distance travelled?
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