Math 1090 Section 5 Test3
Name:
Read all directions carefully and show all your work for full credit.
Each of the following questions is worth 10 points total. Your score on the exam will
consist of the 10 best scores on the following 12 questions taken out of a total of 100
points. Good Luck!!!
8
>
>
<
1. Maximize and minimize the function Z = 3x 5y given the constraints >
>
:
6x + 2y 12
6x + 4y 24
x0
y0
2. If A = 25 16 and B = 47
10 nd AT B T and 2A 3B
3
3. Chester owes Andrew $7000 due in 5 years and $3,000 due in 7 years. If Chester
would like to pay o the debts with a payment of $4000 in 2 years and $x in 6
years how much is x? Assume an interest rate of 7% compounded daily.
2
4. If C = 4
3
2
3
2 5 1
3
5
4
1 3 0 ,D=
2 5, and E = 1 0 1 then nd CDE .
0 1 5
1
5. Rutherford has bought a new car for $30,000. If he decides to make payments
for 5 years at the end of each month and he is charged an interest rate of 4.5%
compounded monthly how much are his payments? What is the nance charge
of this loan?
8
>
>
<
y x1
6. Find all solutions that satisfy all of the following inequalities. > 2y2y +5xx 210
>
:
y + 5x 5
7. Find all solutions to the following system of equations using matrix reduction.
x + 2y + 3z = 9
2x 3y + z = 2
3x 2y 2z = 2
8. Ulysses decides to put $6000 into a savings account that gets an interest rate
of 7% compounded semi-annually(twice a year). What is the eective rate that
Ulysses is getting on the account? How many years will it take the account
balance to reach $7500?
9. Dwight decides that he will invest $30,000 in Tyler INC. Tyler guarantees a cash
ow of $10,000 in 4 years, $15,000 in 5 years, and $12,000 in 8 years. Assuming
an interest rate of 6% compounded annually is the investment protable? (Hint:
Calculate the Net Present Value)
2
10. If F = 1 2
6
1 4 and G = 64
5
2
1
0
3
7
7
5
then nd FG, and GF
2
11. Find the inverse of the matrix H = 4
3
1 3 6
2 5 11 5.
3 10 18
12. Herbert decides that he needs to start saving up for a new car. The car that
he would like to purchase in 7 years will cost $40,000. His mom has already
promised that she will give Herbert $10,000 right now to help him meet his goal.
Herbert also decides to make payments of $R at the begining of each month
into the same account that earns 4% compounded monthly. How much is each
payment?
1. (10pts)
2. (10pts)
3. (10pts)
4. (10pts)
5. (10pts)
6. (10pts)
7. (10pts)
8. (10pts)
9. (10pts)
10. (10pts)
11. (10pts)
12. (10pts)
total