Instructions

Use the following information: Prakash has to decide whether or not to test a batch of 1000 widgets before sending them to the buyer.
In case he decides to test, he has two options:
a) Use test I ;
b) Use test II.

Test I cost Rs. 2 per widget. However, the test is not perfect. It sends 20% of the bad ones to the buyer as good. Test II costs Rs. 3 per widget. It brings out all the bad ones. A defective widget identified before sending can be corrected at a cost of Rs. 25 per widget. All defective widgets are identified at the buyer's end and penalty of Rs. 50 per defective widget has to be paid by Prakash.

Question 67

Prakash should not test if the number of bad widgets in the lot is:

Solution

We should consider three possible cases as 1. when he is using test 1
2. When he is using test 2
3. When he is using no test
Now we will choose a method where the total expenditure will be least.
So for option A, let's consider that number of defective pieces are 50.
Hence, while using test 1:
Cost of testing = $$1000 \times 2 = 2000$$
Correcting 80% of pieces = $$40 \times 25 = 1000$$
Penalty for 20% of pieces = $$10 \times 50 = 500$$
Total = 3500

For test 2:
Cost of testing = $$1000 \times 3 = 3000$$
Correcting all 50 pieces = $$ 50 \times 25 = 1250 $$
Total= 4250

For no test:
Penalty for all 50 pieces = $$ 50 \times 50 = 2500$$

Hence cost is least when he is using no test while number of defective pieces is less than 100.

 


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