A supervisor is contemplating whether or not to investigate labor efficiency variance in the Assembly Department.
It will cost $ 6000 to undertake investigate and another $ 18000 to correct operation. If the department is found to operating improperly. if the department is operating improperly and he failed to make investigation , operating cost from the various inefficiendie are expected to amount $ 33,000/- . The supervisor would be indifferent between investigating and not investigating the variance if te probability of improper operation .
For the investigation the cost is $6000 and there is another $18000 involved in correcting operations. If the operations are not done properly they cost $33000. Now let us say that the probability that the operations are not being carried out properly is P.
Now the probability P which would make the supervisor indifferent to carrying out the investigation is given when
33000P - (1-P)*( 6000+ 18000)=0
=>33000P - (1-P)*( 24000)=0
=>33000P- 24000+ 24000P =0
=> 57000P= 24000
=> P = 24000/57000
=> P = 0.4210
So the probability of the operations being not done properly that make the supervisor indifferent to an investigation is 0.4210
Let p be the probability of superwisor that investigates the labour efficiency variance . Then the resulting cost of investigation and corrrection = $(6000+180000) = $24000
So the expected cost = 24000p.
If the superwisor does not investigate the labour efficiency variance, then the the departmental inefficiency cost = 33000.
So the expected inefficiency cost = 33000*probabilty that superwisor does not investigate= 33000(1-p)
Since the question of indetermacy is when both costs are same.
24000p = 33000(1-p)
24000p = 33000-33000p
P = 33000/(24000+33000)
p = 33/57
p = 11/19 is the probability that superwisor investigate.
Also the probability that the superwisor does not investigate = 1-11/19 = 8/19