07-21-2002, 05:27 PM
Let's say b + g squared = 100. Meaning, for $100, you can recruit 100 brown-eyed 20-something terrorists, 10 blue-eyed granny terrorists, or 5 grannies and 75 be20's each week. The cost of the first granny is 1 be20, the cost of the second granny is 3 be20's, the cost of the third granny is 5 be20's.
Let's say there are 1 million be20's flying each week, and 1 million grannies. If we search nobody, approximately 1 in 10,000 be20's will be terrorists, and probably no grannies will be terrorists. If the benefit to terrorists of taking down a plane is T, they will earn 100 * (T minus 1 dollars).
At what percentage of searches will they begin to recruit grannies? If we search 2 in 3 be20's, they are indifferent to adding a granny. After searching what percentage of be20's should we start searching grannies? Assume, our cost per search is $2, and our cost per downed plane is $1 million.
Our benefit for searching the first be20 is $1 million/10,000, minus $2, or $98. If we search 90% of be20's, and no grannies, 1 granny is worth 10 be20's, and they will add the fifth granny. Our profit for searching the first granny will be $1 million/200,000 minus $2, or $3.
If there are 2 terrorists in a million grannies, we won't search any. So, we won't search our first granny until we have searched 80% of be20's, and a granny is worth 5 be20's. At what point are we indifferent to searching grannies or be20's? When we are known to be searching 6/7 be20's?
Let's say out cost for searching people starts at $2 for the first 1 million, or 1/2 of travelers, rises to $3 for the next 500,000, and goes to $5 for the remaining 500,000. What proportion of be20's versus grannies will be sent against us, how many people should we search, and in what proportions?
eLROY
Let's say there are 1 million be20's flying each week, and 1 million grannies. If we search nobody, approximately 1 in 10,000 be20's will be terrorists, and probably no grannies will be terrorists. If the benefit to terrorists of taking down a plane is T, they will earn 100 * (T minus 1 dollars).
At what percentage of searches will they begin to recruit grannies? If we search 2 in 3 be20's, they are indifferent to adding a granny. After searching what percentage of be20's should we start searching grannies? Assume, our cost per search is $2, and our cost per downed plane is $1 million.
Our benefit for searching the first be20 is $1 million/10,000, minus $2, or $98. If we search 90% of be20's, and no grannies, 1 granny is worth 10 be20's, and they will add the fifth granny. Our profit for searching the first granny will be $1 million/200,000 minus $2, or $3.
If there are 2 terrorists in a million grannies, we won't search any. So, we won't search our first granny until we have searched 80% of be20's, and a granny is worth 5 be20's. At what point are we indifferent to searching grannies or be20's? When we are known to be searching 6/7 be20's?
Let's say out cost for searching people starts at $2 for the first 1 million, or 1/2 of travelers, rises to $3 for the next 500,000, and goes to $5 for the remaining 500,000. What proportion of be20's versus grannies will be sent against us, how many people should we search, and in what proportions?
eLROY