A company is planning to re-equip one of its major production plants and one of two types of machine, the Zeta and the Precision II, is to be purchased. The prices of the two machines are very similar so the choice of machine is to be based on two factors: running costs and reliability. It is agreed that these two factors can be represented by the variables: average weekly operating costs and number of breakdowns in the first year of operation. The company"s production manager estimates that the following probability distributions apply to the two machines. It can be assumed that the probability distributions for operating costs and number of breakdowns are independent.
Average weekly
Zeta
operating costs ($)
Prob.
No. of breakdowns
Prob.
20 000
0.6
$0
0.15
30 000
$0
$1
0.85
Precision II
Average weekly
operating costs ($)
Prob.
No. of breakdowns
Prob.
15 000
0.5
0
0.2
35 000
$1
1
0.7
2
0.1
Details of the manager"s utility functions for operating costs and number of breakdowns are shown below:
Average weekly
operating costs ($)
Utility
No. of breakdowns
Utility
15 000
1
0
1
20 000
0.8
1
0.9
30 000
0.3
2
0
35 000
0
(a) The production manager"s responses to questions reveal that, for him, the two attributes are mutually utility independent. Explain what this means.
(b) The production manager also indicates that for him k1 = 0.7 (where attribute 1 = operating costs) and k2 = 0.5. Discuss how these values could have been determined.
(c) Which machine has the highest expected utility for the production manager?