43. The U.S. government wants to determine whetherimmigrants should be tested for a contagious disease,and it is planning to base this decision on financialconsiderations. Assume that each immigrant who isallowed to enter the United States and has the diseasecosts the country $100,000. Also, assume that eachimmigrant who is allowed to enter the United Statesand does not have the disease will contribute $10,000to the national economy. Finally, assume that x percentof all potential immigrants have the disease. The U.S.government can choose to admit all immigrants, admitno immigrants, or test immigrants for the diseasebefore determining whether they should be admitted. Itcosts T dollars to test a person for the disease, and thetest result is either positive or negative. A person who does not have the disease always tests negative. However, 10% of all people who do have the disease testnegative. The government’s goal is to maximize theexpected net financial benefits per potential immigrant.a. If x 5 5, what is the largest value of T at whichthe U.S. government will choose to test potentialimmigrants for the disease?b. How does your answer to the question in part achange if x increases to 10?c. If x 5 5 and T 5 $500, what is the government’soptimal strategy?
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
43. The U.S. government wants to determine whether
immigrants should be tested for a contagious disease,
and it is planning to base this decision on financial
considerations. Assume that each immigrant who is
allowed to enter the United States and has the disease
costs the country $100,000. Also, assume that each
immigrant who is allowed to enter the United States
and does not have the disease will contribute $10,000
to the national economy. Finally, assume that x percent
of all potential immigrants have the disease. The U.S.
government can choose to admit all immigrants, admit
no immigrants, or test immigrants for the disease
before determining whether they should be admitted. It
costs T dollars to test a person for the disease, and the
test result is either positive or negative. A person who does not have the disease always tests negative. However, 10% of all people who do have the disease test
negative. The government’s goal is to maximize the
expected net financial benefits per potential immigrant.
a. If x 5 5, what is the largest value of T at which
the U.S. government will choose to test potential
immigrants for the disease?
b. How does your answer to the question in part a
change if x increases to 10?
c. If x 5 5 and T 5 $500, what is the government’s
optimal strategy?
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