Construction of precast concrete products involves the employment of specialist teams of fixers (to prepare the metal reinforcing bars and couplers), pourers (to place the reinforcing materials in the moulds and pour the concrete) and strikers (to strike and clean the moulds). The Brisbane plant at GC Casting has five production lines that are used to produce concrete road barriers. The personnel employed on each line have different levels of experience, and their salaries vary accordingly. In order to assess the performance of each production line, an analyst has collected data on the number of employees of each type, their average annual salaries, and the number of road barriers produced in a given year. The data are reported in Table 2. Assume the production frontier exhibits VRS.

(a) (6 marks) Determine the input-oriented technical efficiency (ITE), cost-allocative efficiency (CAE) and cost efficiency (CE) of Line D. How technically efficient was Line D?

(b) (3 marks) Suppose input mixes are fixed. How many employees of each type should have been employed on Line D if it was to have produced the same number of barriers and be regarded as technically efficient?

(c) (6 marks) Suppose inputs and outputs can be chosen freely. Find the inputs and outputs that Line D should have targeted if it had wanted to be regarded as fully technically efficient but not necessarily cost efficient. What other production lines should the manager of Line D have studied if he/she had wanted to reach those targets?

(d) (3 marks) Identify the input quantities that would have minimised the cost of producing the outputs that were produced by Line D.

Table 2: Data for Concrete Barrier Production Lines Line A Line B Line C Line D Line E Quantities mo.) Barriers 300 331 212 300 310 Fixers 5 4 6 6 4 Pourers 8 7 9 10 10 Strikers 2 2 3 3 3 Average Annual Salaries ($000) Fixers 42 T4 80 3'? 48 Pourers 35 T0 60 50 45 Strikers 33 50 41 45 50