Sample Questions for Final

1. Solve the following. You may use any method.
2. The Ace Truck Leasing Company leases a certain size truck for $30 a day and 15 cents a mile, whereas the Acme Truck Leasing Company leases the same size truck for $25 a day and 20 cents a mile. Find linear functions which describing the daily cost of leasing a truck from each company. If you plan to drive 70 miles, which company would you lease a truck from? For a one day rental how many miles would you have to drive in order for the leasing costs to be the same from either Acme or Ace?
3. The freezing point of water is Fahrenheit (F) which is equal to Kelvin (K). The boiling point is F ( K).
4. Let , , ,
   , and .
   Find EA, AE, AB, BA, C+D, A+D, 12C-E.
5. William, who is a very big eater, had 3 cheeseburgers, 2 orders of fries and 3 milk shakes for lunch on Tuesday. All this cost him . Wednesday he spent only and purchased 2 cheeseburgers, 3 orders of fries and 2 milk shakes. For lunch on Thursday William spent on 4 cheeseburgers, 3 orders of fries and 3 milk shakes. Find the cost of a single cheeseburger, an order of fries or one milk shake.
6. A farmer has 200 acres on which to plant two crops, peanuts and soybeans. It costs per acre to produce peanuts, per acre to produce soybeans, and there is available to pay for this years production. If the yield is 200 bushels of peanuts or 60 bushels of soybeans, and if the farmer has contracted to store at least 24,000 bushels of combined soybeans and peanuts, how much of each should the farmer plant to maximixe the profits when the net profit on a bushel of peanuts is and the net profit for 3 bushels of soybeans is .
   Find the objective function and the system of constraint equations.
7. Determine, for each tableau, whether or not it is in final form. If it is in final form write the solution. If it is not in final form, choose and circle a pivot element. (DO NOT PIVOT) (10 pts)

   

   

   

   

8. Graph the feasible region and find ALL corner points for the following constraint equations. (9 pts)
   

   

   

9. A Dentist rewards children who visit the dental clinic with prizes from two different prize boxes. The blue prize box contains 15 super balls and 9 whistles. The red prize box contains 11 super balls and 13 whistles. After a visit to the dentist a child selects a prize box at random then randomly selects a prize from that prize box. What is the probability that a whistle is picked from the red box?
10. In a survey of 120 customers at a local sporting goods store the following data were determined: (The survey asked the customers which, if any, of the NBA teams in Texas they followed)
    12 of them said they follow only the Dallas Mavericks
    25 of them said they follow only the Houston Rockets
    26 of them said they only follow the San Antonio Spurs
    15 of them said they follow both the Mavericks and the Rockets
    10 of them said they follow both the Mavericks and the Spurs
    12 of them said they follow both the Rockets and the Spurs
    8 of them said they follow all three teams.
    How many of these sports fans follow

    a. at least one of these teams?

    b. the Rockets and the Mavericks but not the Spurs?

    c. the Spurs?

    d. none of them?

    e. What is the probability that a randomly selected fan follows either the Rockets or the Spurs?

    f. What is the probability that a randomly selected fan will be a follow the Mavericks?

11. How many 7-digit telephone numbers are possible if the first digit must be non-zero?
12. An exam consists of 10 true or false questions. Assuming that every question is answered, in how many different ways can a student complete the exam? What is the probability that the student gets at least 9 of the answers correct?
13. Honeynut Inc. sells roasted peanuts in 14 oz containers. The quality control department at Honeynut has determined that the actual content weigth was normally distributed with a mean, of 13.9 oz and a standard deviation, of .2 oz. Based on this information what is the probability that a container of roasted peanuts:

    a. Will weigh at least 14 oz.?

    b. Will weigh between 13.8 and 14.2 oz.?

14. In a lottery 5,000 tickets are sold for $1 each. One first prize of $2,000, 2 second prizes of $500, 5 third prizes of $100 and 10 consolation prizes of $10 are to be awarded. What are the expected earnings of a person who buys one ticket?
15. Honest Al's Car Parts has found that the automobile batteries it sells have a normally distributed life expectency with a mean of 50 months and a standard deviation of 3 months.

    a. What is the probability that one of these batteries will last for at least 56 months?

    b. What is the probability that one of these batteries will last for between 46 and 54 months?

    c. If Honest Al sells these batteries with a 44 month warranty what percentage of them will be returned for a warranty adjustment?

16. Three marbles are selected at random without replacement from a jar containing three white marbles and four blue marbles. Let X denote the number of blue marbles drawn.

    a. Write the sample space for this experiment.

    b. Is each outcome equally likely?

    c. Find the probability distribution of X and draw a Histogram representing this distribution.

    d. Find the standard deviation of X.

17. You have borrowed $5000 from a friend. If you pay him $100 at the end of each month and he charges you 4% compounded monthly:
    1. How long will it take you to pay him back? (4 pts)
    2. How much interest will you have paid? (4 pts)
18. Your grandparents put some money in a trust fund 21 years ago; it is currently worth $25,000.
    1. If the interest rate was 4% compounded monthly, how much money did they deposit? (4 pts)
    2. If the interest rate was 4% compounded monthly for the first 7 seven years and 6% compounded monthly the next 14 years, how much money did they deposit? (5 pts)

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