Math 141                                                                Practice 2                                                                          



1.
Find the point of intersection of the lines whose equations are 4x + 2y = 12 and 3x + 9y = 39.
A.
(5, –4)
B.
(10, 1)
C.
(1, 4)
D.
(2, 2)


2.
Graph the constraint inequalities for a linear programming problem shown below. Which feasible region shown is correct?
 
2 x + 3y ≤ 12
 
x 0, y ≥ 0



3.
Write the constraint inequalities for this situation: Kim and Lynn produce pottery vases and bowls. A vase requires 35 oz. of clay and 5 oz. of glaze. A bowl requires 20 oz. of clay and 10 oz. of glaze. There are 500 oz. of clay available and 200 oz. of glaze available. The profit on one vase is $5 and the profit on one bowl is $4.
A.
35x + 5y ≤ 5, 20 x + 10y ≤ 4, x ≥ 0, y ≥ 0
B.
35x + 5y ≤ 500, 20 x + 10y ≤ 200, x ≥ 0, y ≥ 0
C.
35x + 20y ≤ 500, 5 x + 10y ≤ 200, x ≥ 0, y ≥ 0
D.
35x + 20y ≤ $5, 5 x + 10y ≤ $4, x ≥ 0, y ≥ 0


4.
The graph of the feasible region for a mixture problem is shown below. Find the point that maximizes the profit function P = 2x + y.

A.
(0, 2)
B.
(2, 4)
C.
(4, 1)
D.
(3, 0)


5.
Find an initial solution using the Northwest Corner Rule and compute its total transportation cost.
 
Shop1
Shop 2
Shop 3
 
Bakery 1
        3
 
        1
 
         2
 
 
5
Bakery 2
        1
 
        5
 
         4
 
6
 
3
5
3
rim conditions


6.
Suppose you invest in an account that pays 6% interest, compounded quarterly. You would like your investment to grow to $8000 in 14 years. How much would you have to invest in order for this to happen?
A.
$2125
B.
$2290
C.
$2650
D.
$3475


7.
What is the APY for 6% compounded weekly?
A.
6.00%
B.
6.09%
C.
6.18%
D.
7.25%


8.
A man cuts back on his latte habit and instead makes $20 deposits each month into a savings account earning 6% interest compounded monthly. He continues these deposits for eight years. How much will the account be worth after eight years?
A.
$1920
B.
$2457
C.
$2941
D.
$3250


9.
John bought a house in 1947 for $19,000 and sold it in 1997. If the 1947 CPI is 22.3 and the 1997 CPI is 160.5, how much would the house be worth in 1997 dollars?
A.
$136,749
B.
$101,086
C.
$94,921
D.
$25,356


10.
Five years after paying $8000 for some shares of a risky stock, you sell the shares for $4500 (at a loss). Compute the annual returrn to the nearest percent.
A.
-9%
B.
-11%
C.
-14%
D.
-18%


11.
A GreatCity municipal bond with face value $100 currently trades at 107.5 points and yields 6.8%. What is the coupon rate?
A.
6.8%
B.
7.31%
C.
7.5%
D.
5.1%


12.
The average annual inflation rate over the next 5 years is projected to be about 3.4%. What is the present value of $1 in 5 years?
A.
84 cents
B.
85 cents
C.
86 cents
D.
87 cents


13.
In early 2002 the inflation rate was about 1.4%. If you invested in a savings account with an annual interest rate of 4.8%, what was the real growth rate of this investment?
A.
1.66%
B.
3.35%
C.
4.27%
D.
6.12%


14.
Pat invested in her employer's stock program in 1981. The annual yield for her investment was 6.5%, but the inflation rate was 7.8%. What was the real growth rate of this investment?
A.
–1.21%
B.
–2.09%
C.
–3.30%
D.
–4.41%


15.
This table describes the share prices of the fictional mutual funds ABC and XYZ:
Fund
Jan 1st
Apr 1st
ABC
$20
$18
XYZ
$50
$55
Suppose that you invest $100 in ABC and $200 in XYZ on Jan 1st. What is your
investment worth on April 1st?
A.
$310
B.
$300
C.
$73
D.
$303


16.
Ellie takes out a conventional loan to purchase a car. The interest rate is 7.5% compounded monthly and Ellie has four years to repay the $12,000 she borrowed. What are Ellie's monthly payments?
A.
$95.46
B.
$139.33
C.
$169.53
D.
$290.15


17.
You take out a 30 year fixed rate mortgage of $180,000 at an APR of 5.2%. Find the monthly payment and the total payment.
A.
$988.40 and $355,824
B.
$988.40 and $180,000
C.
$500 and $180,000
D.
$780.40 and $280,800


18.
You take out a 30 year fixed rate mortgage of $180,000 at an APR of 5.2%. Find the interest portion of mortgage payment in the first month.
A.
$780
B.
$988.40
C.
208.40
D.
488.40


19.
Suppose you are married filing separately with two dependent children, and you had a taxable income of $38,600 in 2006. Assuming you are not entitled to a tax credit for either child, how much income tax did you pay?
A.
$9,650
B.
$15,002.5
C.
$6,207.5
D.
other amount


20.
Kathrin earns $2500 after tax and her parents support her to the tune of $300 a month. She lives in San Francisco and her rent is $1200. Her other housekeeping costs are $300 (food), $350 (entertainment), 200 (clothing), 180 (transportation). She is also paying off old medical bills: $300 a month. At the end of the month, she has
A.
a surplus of $270.
B.
a deficit of $30.
C.
a deficit of $2530.
D.
a surplus of $2800.


Answer Key

1. C
2.
A
3. C
4. C
5.
 
Shop1
Shop 2
Shop 3
 
Bakery 1
        3
3
        1
2
         2
0
 
5
Bakery 2
        1
0
        5
3
         4
3
6
 
3
5
3
rim conditions

Transportation Cost: 3*3+2*1+3*5+3*4 = 38
6. D
7. C
8. B
9. A
10. B
11. B
12. B
13. B
14. A
15. A
16. D
17. A
18. A
19. C
20. A