# 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...

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 .

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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

(24000+33000)p =33000

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