problem about logic?

Question

A manufacturing factory produces a product, which can get the profit of $1000 for every unit that sold (that unit is non-defective). The factory produces 11 units of that product with one defective unit. In order to find the defective unit, the factory uses an investigating scheme on production items before they are sold.

The investigating scheme as follow:
- More than one unit can be checked for every single checking process.
- Every single checking process will cost $1000.
- After the checking process, each of the non-defective product can be sold and gain the profit of $1000.
- During the checking process, if the defective unit is investigated, all the units in that checking process will be considered as defective item and cannot be sold.

Based on the investigating scheme, what is the best strategy for the factory so that they can gain the maximum profit even in the worst situation. Find the profit that they can gain (in the worst situation).

Answer 1

1 process in a group of 11 makes profit of -1000
2 process (5, 6) profit 3000 to 4000
3 process (4, 4, 3) profit 4000 to 5000
4 process (3, 3, 3, 2) profit 4000 to 5000
5 process (2, 2, 2, 2, 3) profit 3000 to 4000
6 process (2, 2, 2, 2, 2, 1) profit 3000 to 4000
7 process (2, 2, 2, 2, 1, 1, 1) profit 2000 to 3000
8 process (2, 2, 2, 1, 1, 1, 1, 1) profit 1000 to 2000

Best stratergy is (4, 4, 3) or (3, 3, 3, 2) which gain profit 4000 in worst situation.

Answer 2

The information in this problem is incomplete.

First off if you make $1000 profit, then the total sale of the product is most likely some where between $3000 and $4000 which means that you will take a $4000 dollar hit right of the bet, if 1 unit is defective (unless you consider the repair or assembly process to be free).

Next, it sounds to me like you stand to make no money because defects are not acceptable. If you find a defect, you must have investigation and then you can't sell anything. You have made 2 contradicting statements in that part of logic. You must either have two different processes for checking , or one process clearly defined.

I'm assuming also that the defect can be caused by multiple things in this product, so you would have to either put in pre-checks, or post checks to remove faulty components. Until this happens you must check 100% (so, you're back to making nothing). You could check one unit out of the bunch, but then you are expecting to have recalls and field problems. This will become much more expensive than what you make.