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KOC¸ UNIVERSITY
MATH 101 - FINITE MATHEMATICS
Final Exam January 8, 2008
Duration of Exam: 140 minutes
INSTRUCTIONS: CALCULATORS ARE ALLOWED FOR THIS EXAM.
No books, no notes, no questions and no talking allowed. You must always explain your answers and show your work to receive full credit. Use the back of these pages if necessary. Print (use CAPITAL LETTERS) and sign your name, and indicate your section below.
Surname, Name: —————————————————
Signature: ————————————————————
Section (Check One):
Section 1: S. K¨u¸c¨uk¸cif¸ci (Tue-Thu 11:00) —– Section 2: S. K¨u¸c¨uk¸cif¸ci (Tue-Thu 14:00) —– Section 3: M. Sarıdereli (Mon-Wed 14:00) —– Section 4: M. Sarıdereli (Tue-Thu 11:00) —– Section 5: E. S¸. Yazıcı (Tue-Thu 12:30) —–
PROBLEM POINTS SCORE
TOTAL 150
- Find the following limits if they exist. Specify any infinite limits.
(a) (5 points) lim r→ 9
r (r − 9)^4
(b) (5 points) lim x→ 0
1 − x^2 x
(c) (5 points) lim x→ 10 −^ ln(100 − x^2 ) =
(d) (5 points) lim x→∞
3 x^2 − 1 x − 1
(e) (5 points) lim x→ 4
4 − x | 4 − x|
A list of formulas: I = P rt; A = P (1 + rt) A = P (1 + i)n; AP Y = (1 + (^) mr )m^ − 1 F V = P M T (1+i)
n− 1 i , where^ i^ =^
r m and^ n^ =^ mt P V = P M T 1 −(1+i)
−n i
- You need 24, 000 YTL. A friend is willing to lend you this amount, but he wants 27 , 000 YTL after one year. You could also borrow 24, 000 YTL from Kazıkbank at 16% compounded monthly, to be paid back with monthly payments in one year. (a) (6 points) What would be your monthly payments to Kazıkbank?
(b) (5 points) What would be the total interest you pay to Kazıkbank?
(c) (6 points) If you borrow from your friend, you could open an account at Cimribank in order to save money (para biriktirmek). How much would you have to deposit every month into an account at 8% compounded monthly to accumulate 27, 000 YTL in one year?
(d) (3 points) Do you borrow 24, 000 YTL from your friend or from Kazıkbank?
- (a) (14 points) Find (A−^1 )B, where
A =
and B =
.
(b) (6 points) Solve
x 1 − 3 x 2 + x 3 = − 1 −x 1 + 4x 2 = 1 x 2 + 2x 3 = 2
- (a) (12 points) Solve the following problem by the geometric approach:
Maximize P = 10x 1 + 5x 2 subject to 4 x 1 + x 2 ≤ 28 2 x 1 + x 2 ≥ 14 x 1 + x 2 ≤ 15 x 1 ≥ 0 , x 2 ≥ 0
(b) (8 points) Formulate the following problem as a linear programming problem (DO NOT SOLVE): A company planning an advertising campaign to attract new customers wants to place a total of at most 10 ads in 3 newspapers. Each ad in the newspaper AA costs 200 YTL and will be read by 2000 people. Each ad in the newspaper BB costs 200 YTL and will be read by 500 people. Each ad in the newspaper CC costs 100Y T L and will be read by 1500 people. The newspaper CC will not accept more than 4 ads from the company. The company wants at least 16000 people to read its ads. How many ads should it place in each paper in order to minimize the advertising costs?
(c) (12 points) Solve the following problem:
- Maximize P = 5x 1 + 3x 2 − 3 x
- subject to x 1 − x 2 + 2x 3 ≤
