Name __________________
Period _____
MAT 217 Final Review
Extra Credit
Honors Brief Calc.
1. What combination of products x and y maximizes the profit function P  70 x  50 y given the
2 x  y  40
following constraints:
?
x  y  32
2. Suppose that if a person with tuberculosis is given a TB screening, the probability that his or her
condition will be detected is 0.90. If a person without tuberculosis is given a TB screening, the
probability that he or she will be diagnosed incorrectly as having tuberculosis is 0.3. Suppose, further,
that 11% of the adult residents of a certain city have tuberculosis. If one of these adults is diagnosed as
having tuberculosis based on the screening, what is the probability that he or she actually has
tuberculosis?
3. A company produces end tables and cocktail tables. An end table requires 2 hours of sanding and 2
hours of varnishing. A cocktail table requires 4 hours of sanding and 2 hours of varnishing. The
equipment required for each can be used on one table at a time. The sanding equipment will run at most
120 hours, and the varnishing equipment will run at most 80 hours. Use the Simplex Tableau to find the
maximum profit and the number of each type of table when the profit for each end table is $30 and the
profit for each cocktail table is $40.
4. Nine people are to line up for a group photograph. If two of them refuse to stand next to each other,
in how many different ways can the photo be taken?
5. Use   np and   npq and the normal approximation to the binomial distribution to find the
probability that at skeet shooter hits at least 160 of 200 targets when the probability of hitting any one
target is 0.75.
6. Elena deposited $115 a month into an account at 7% compounded monthly for 20 years. What is the
largest amount she may withdraw monthly for the next 12 years?
7. A wine taster claims to be able to distinguish between two types of wine 65% of the time. You give
her 12 glasses of wine and tell her you will grant her claim if she correctly identifies at least 9 of the 12
glasses. What is the probability her claim is justified, but does not pass?
8. A family decides to purchase a $220,000 home and take out a loan at 8% for 25 years.
a) What is their monthly payment?
b) What is the total amount they will pay for their home?
2 x  3 y  4 z  7
9. Solve 
.
 x  2 y  3z  2
10. In a survey of 1118 students at a small western college, it was found that:
 240 students are seniors
 563 students are female
 196 students are on the dean’s list
 121 students are female and a senior
 34 students are seniors and on the dean’s list
 97 students are females and on the dean’s list
 24 students are female seniors on the dean’s list
How many students are not a senior, female, or on the dean’s list?
How many students are on the dean’s list but are not female or a senior?