In Class Final Exam Review Math 141
1. Demand and Supply. The market will demand at most 1000 units of a certain product even if it is free. For each decrease of $5 in the price, the demand increases by 10 units. Suppliers will provide none at a price of $200. They will provide 1600 units at a price of $600 per unit. Find the equilibrium point.
2. The table shows the mean price of homes in thousands of dollars in a certain city neighborhood for different years. Find the linear regression equation for the mean price as a function of the number of years past 1997. What does the equation predict for the year 2010?
Year 1997 2000 2003 2004 2006
Mean price
In $1000s 70 74 85 86 90
3. 
a) Find 
b)
Find AB
4. A farmer plants two crops, A and B. Each acre of A uses $35 for seed and fertilizer. Each acre of B uses $25 for seed and fertilizer. Each acre of A requires 40 labor hours and each acre of B requires 30 labor hours. He plans to plant 20 acres of A and 45 acres of B.
a) Write a product of two matrices showing the total cost and labor hours.
b) If labor costs $15 per hour, what matrix product shows the total cost?
5. Each matrix is the rref form of the augmented matrix for a system of equations. Solve each system or state no solution. If the solution is infinite, give two particular solutions.
a) 
b) 
c) 
6. When can a system be solved using an inverse matrix? Using rref?
7. 
Solve the matrix
equation AX + 4X=B for X.
8. Leontief input-output
An economy is based on 2 sectors’ energy and manufacturing. Each dollar of energy production uses $0.20 of energy and $0.30 of manufacturing. Each dollar of manufacturing uses $0.40 of energy and $0.15 of manufacturing. How much of each should be produced to meet a demand for $30 million dollars of energy and $12 million dollars of manufacturing? How much of each sector is used up in the production process?
9. Graph the region described by 
10. A company produces two products, A and B. Each unit of A requires 2 hours in the parts dept., 1 hour in assembly and 1 hour in finishing. Each unit of B requires 3 hours in the parts dept., 1 hour in assembly and 2 hours in finishing. They have available 30 hours in parts, 13 hours in assembly and 18 hours in finishing. How many of each should they produce to maximize profit if :
a) profits per unit of A and B are $20 and $45 respectively.
b) profits per unit of A and B are $30 for each.
c) profits per unit of A and B are $30 and $25 respectively.
11. 40 people were asked if they run, walk or swim for exercise.
A total of 20 run but 10 said they only run.
2 only swim.
6 walk and swim but do not run.
5 do all 3 types of exercise.
7 run and swim.
26 walk or swim.
How many do none of the three?
12. A builder has 10 lots on which to build 3 spec homes. How many ways can he decide where to build if :
a) the homes are identical?
b) the homes are all different?
c) two of the homes are identical and the 3rd is different.
13. How many ways can you assign 5 new cases to some of 8 lawyers if each case needs exactly one lawyer and
a) any lawyer can work any number of cases?
b) no lawyer works on more than one case?
14. A box contains 5 red balls and 7 blue balls and 3 yellow balls. A person randomly selects 4 all at once.
a) Find the probability that exactly 2 red or exactly 2 blue are chosen.
b) Find the conditional probability that at exactly 2 blue are chosen given at least one red is chosen.
15. A company manufactures its product on each of 3 machines. The portion produced and the probability of a defective product for each machine is shown.
Portion of total production. Probability of defective
Machine I 0.40 0.020
Machine II 0.25 0.025
Machine III 0.35 0.030
a) Find the probability that a randomly selected product is defective.
b) Find the probability that a product produced by machine III is defective.
c) Find the probability that a defective product was produced by machine III.
16. A box contains 4 red and 3 blue balls. A person chooses 3 all at once. X is the number of blue balls chosen. Write the distribution of X. Find E(X) showing all work.
17. A box contains 6 red and 3 blue balls. A person chooses one at a time until he gets a red ball. X is the number of blue balls chosen. Write the distribution of X and find E(X).
18. A stock was watched for 5 consecutive days. The price per share on each day is shown.
Day 1 2 3 4 5
$/share 15.76 15.90 16.15 16.00 15.90
Find the mean, median, mode and standard deviation of the price per share for these 5 days.
19. A quiz was given to a group of students. The scores and frequencies are shown.
Score 0 1 2 3 4 5
# students 2 3 6 8 7 7
Find the mean, median, mode and standard deviation for the scores.
20. A box contains 8 red and 12 blue balls. A person selects one ball and puts it back. This done 30 times. X is the number of times the ball is red.
a) Find the probability that X is equal to its expected value.
b) Find 
.
c) Find the normal approximation to the probability in part b.
Find the probability that a randomly selected woman in this age group is
a) between 63 and 67 inches.
b) at least 64 inches.
c) at most 64 inches.
Find a height so that the expected portion of women who are
d) at least this height is 0.20.
e) at most this height is 0.40.
Be sure to do the Finance review and suggested problems for 9.1 and 9.2.