Math 115 Name_______________________________

Finite Mathematics

Final Exam

Be sure to show all relevant work. Points will be deducted for omitted work!

1. The Par Busters Golf Company can manufacture 2,000 of its most popular

drivers at a cost of $125,000. To manufacture 8,000 drivers the cost is

$341,000. (12 pts)

a. Write a linear cost function for the manufacture of the driver.

b. Find the break even point if the driver retails for $75?

2. Consider the following system of linear equations. x - 2y + z = 3

2x - y + 2z = 0

3y - 2z = -3

Use the Gauss-Jordan method of matrix reduction to solve the system.

Indicate each row operation and show each intermediate matrix. (8 pts)

3. Consider the following question.

$80,000 has been invested in three ways: in a tax-free bond fund paying 7.5%, in a certificate of deposit paying 8%, and in a stock fund paying 11%. The amount in the stock fund is twice the amount invested in the bond fund. The total annual interest on these investments is $7,455. How much is in each investment?

Write, but do not solve, a system of three equations in three variables that could be used to answer this question. Clearly define the three variables! (8 pts)

4. Perform the indicated operations. (12 pts)

a.

b.

5. Graph the feasible region for the following system of linear inequalities. Indicate all the corner points of the region.

(8 pts)

2x + y £ 8

10x + 3y £ 30

x ³ 0

y ³ 0

6. A citrus producer has no more than 48 acres of land available for growing oranges and grapefruits. Profits per acre of oranges is $40 while profit per acre of grapefruits is $30. The total labor time available during production is 80 hours. An acre of oranges requires 2 hours of labor and an acre of grapefruits requires 1 hour. Use the simplex method to determine the number of acres of oranges and the number of acres of grapefruits that will maximize the producers profits, and determine the maximum profit. (8 pts)

7. Let U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 3, 4, 5, 7}, B = {0,1, 2, 5, 8, 9}. List the elements in the following sets. (10 pts)

a. A Ç B

b. È B

8. Suppose that P(A) = .36, P(B) = .25, and P(A È B) = .52. Determine the following. (12 pts)

a. P(A Ç B) =

b. P(B çA) =

c. Are A and B mutually exclusive? Explain.

9. a. A single card is drawn from a standard deck of 52 cards. What is the probability that it is a face card or a red card? (6 pts)

b. Two cards are drawn without replacement from a standard deck of 52 cards.

What is the probability that they are both hearts? (6 pts)

10. Suppose that you have 2 jars containing the following: jar 1 has 3 red and 3 green

marbles, jar 2 has 2 red and 3 green marbles. A jar is selected and then a marble is drawn from that jar. The probabilities of selecting jar 1 or 2 are respectively .6 and .4. If a red marble is drawn, find the probability that it came from jar 2. Use a tree diagram and Bayes’ Theorem to get your solution.

(9 pts)

11. A student has 3 math books, 3 poetry books, and 4 history books. He wishes to

arrange these books on a shelf over his desk. In how many different ways can these books be arranged if the poetry books are put in the first three positions?

(6 pts)

12. A ski club consisting of 7 women and 5 men must form a rules committee of 5 members. (12 pts)

a. In how many ways can this committee be selected?

b. What is the probability that the committee will have more men than women?

13. A single fair die is rolled 8 times. What is the probability of getting a number

greater than 4 exactly 3 times? (6 pts)

14. You have a bag containing 6 red marbles and 4 green marbles. Without looking you reach in the bag and randomly grab 2 marbles. Let the random variable, X, be the number of green marbles you get.

a. Write a probability distribution for the random variable X. (6 pts)

b. What is the expected value for the probability distribution in part (a)?

(6 pts)