Name and PID:
STOR 113.006 Practice Final Exam
December 9, 2011
1. The exam duration is 3 hours.
2. There are 13 problems in total. Show your work on all the problems
IN YOUR BLUE
BOOK(s)
to receive full/partial credit.
3. The exam is out of 80 points.
4. You do not have to find the final decimal answers to the problems, you can leave them as
fractions, exponential or logarithmic form.
Honor pledge.
I have not taken or given any unauthorized assistance on this exam.
Signature.
Question 1.
(10 points)
min
f
(
x, y
) =
x
2

6
x
+
y
2

6
y
subject to
x
+
y
≤
4
, x
≥
0
, y
≥
0
.
Question 2.
(10 points)
min
f
(
x, y, z
) =
x
2
+
y
2
+
z
2
subject to
z
=
x
2
+
y

5
.
Question 3.
(5 points) We buy a property in a booming area, and we find that in 10 years it
is worth 1.5 times of its initial value. Assuming that it appreciated by the same percentage
every year, in how many years will it be worth twice its original value?
Question 4.
(4 points) Princess Candlea loves playing with big candles (no pun intended).
One day she accidentally burns the robe of evil magician Evilla. Evilla gets angry, and curses
her to die when her candle burns out.
1. Her candle is 12 inches long right now, and burning @ 1 inch per hour. What is the
candle size as a function of time? How long does she have to live?
Her aunt, Benevolenta is a a nice magician. So Candlea runs to her for help. Evilla’s spell
is strong, so Benevolenta can not remove it. But she puts another spell on the candle. That
it will burn at an exponential rate with half being removed every 1 year.
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 Spring '07
 Codrin
 Truck, Inch

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