NAME:
QUIZ Section:
STUDENT ID:
MATH 111 Final Exam, Winter 2013
HONOR STATEMENT
”I affirm that my work upholds the highest standards of honesty and academic integrity at the
University of Washington, and that I have neither given nor received any unauthorized assistance
on this exam.”
SIGNATURE:
• Do not open the test until instructed to do so. Please turn your cell phone OFF now.
• This exam consists of this cover sheet followed by eight problems on eight pages.
When the test starts, check that you have a complete exam.
• This exam is closed book. You may use one double-sided, handwritten 8 12 × 11 page of notes,
a ruler, and a calculator. Put everything else away. You may not share notes.
• Unless otherwise indicated, you must show your work and justify your answers.
The correct answer with incomplete or missing supporting work may result in
no credit. If you use a guess-and-check method when a better method is available, you may
not receive full credit. On graph-based problems, show your work clearly by marking all lines
and points that you use.
• Place your final answer in the indicated spaces. Unless otherwise specified, you may round
your final answer to two digits after the decimal. Do NOT round off before your final answer.
• If you need more room, use the backs of the pages and indicate to the grader that you have
done so.
Problem
Total Points
1
10
2
10
3
15
4
13
5
12
6
12
7
16
8
12
Total
100
Score
Math 111
Final Exam
Winter 2013
1. (10 points) You produce and sell Things. The graph below shows your total cost (T C) and
your variable cost (V C). Draw and label all lines you use to answer the following questions.
(a) Estimate the average cost at q = 700 Things.
ANSWER: $
per Thing
(b) Compute the Shutdown Price.
per Thing
ANSWER: SDP = $
(c) Estimate T C(701) − T C(700).
ANSWER: $
(d) Find the largest range of quantities that result in an average cost (AC) of no more than
$0.75 per Thing
ANSWER: From q =
to q =
Things
(e) If you sell Things at a price of $0.75 each, name the largest quantity at which you do
not lose money.
ANSWER: At q =
Things
Math 111
Final Exam
Winter 2013
2. (10 points) You produce and sell Things. The graph below shows your marginal cost (M C),
average cost (AC), and average variable cost (AV C).
10
MC
8
AC
6
AVC
dollars per Thing
4
2
0
0
1000
2000
3000
quantity (in Things)
4000
5000
(a) What is the total cost (T C) of producing 3500 Things?
ANSWER: $
(b) What is the shutdown price (SDP )?
ANSWER: $
per Thing
ANSWER: $
per Thing
(c) Estimate T C(1001) − T C(1000)
(d) (4 pts) Suppose each Thing sells at a price of $7 per Thing. How many Things should
you sell in order to maximize the profit, and what will the maximum profit be?
ANSWER: q =
Things; Max profit =$
Math 111
Final Exam
Winter 2013
3. (15 points) You produce and sell Blivets. The price per Blivet, p, is a linear function of the
quantity q of Blivets ordered. You charge p = $24 per Blivet for an order of q = 1 Blivet,
and p = $18 per each Blivet for an order of q = 13 Blivets.
(a) (4 pts) Find the linear formula for price per Blivet, as a function of quantity q ordered.
ANSWER: p =
(b) (2 pts) The Blivets cost $5 each to manufacture and you have fixed costs of $100. Give
the formula for the total cost (TC) to produce q Blivets, as a function of q.
ANSWER: T C(q) =
(c) (3 pts) At what quantity q is the average cost (AC) equal to $7.50/Blivet?
ANSWER: At q =
Blivets
(d) (6 pts) What is the maximum profit? (Assume that you cannot sell a fraction of a
Blivet. The quantity that maximizes profit must be a whole number.)
ANSWER: Maximum profit is
dollars
Math 111
Final Exam
Winter 2013
4. (13 points) You have a budget of up to $120 to spend on pizza for a party you are planning.
There are two types of pizzas your wish to buy: VeggieHeaven and MeatGalore.
Each VeggieHeaven pizza costs $10 and feeds 4 people. Each MeatGalore pizza costs $15
and feeds 6.5 people. Some of your friends are vegetarians, so you must buy at least 2
VeggieHeaven pizzas. The pizza place says they only have enough ingredients left for 6 more
MeatGalore pizzas, so you can buy at most 6 MeatGalore pizzas.
Let x denote the number of VeggieHeaven and let y denote the number of MeatGalore pizzas
you buy. You want to maximize the number of people P (x, y) you can feed, subject to the
given constraints.
(a) (2 pts) Find the formula for your objective function P (x, y). No need to justify.
ANSWER: P (x, y) =
(b) (4 pts) Write the inequalities for your constraints.
(c) (4 pts) Sketch and shade the feasible region. Compute and label the coordinates of all
its vertices.
(d) (3 pts) Find the maximum number of people you can feed, and how many pizzas of each
kind you should order. Show all work.
ANSWER: Can feed a max of
x=
people by ordering
VHs and y =
MGs
Math 111
Final Exam
Winter 2013
5. (12 pts) Two functions vary with time t according to the formulas:
f (t) = 2t2 − 100t + 2400
g(t) = −t2 + 80t
(a) Compute a formula in terms of t for g(t + 2) − g(t). Simplify as far as possible.
ANSWER: g(t + 2) − g(t) =
(b) What is the longest time interval, if any, over which both functions are increasing?
Justify your answer.
ANSWER: From t =
to t =
.
(c) Find all the times t when the graph of g(t) is 200 units higher than the graph of f (t).
ANSWER: At t =
(list all)
Math 111
Final Exam
Winter 2013
6. (12 points) Ann and Bob start a month of intense training for the Tour de France (a famous
bicycle competition). On the first day of training, Ann bikes 50 km, while Bob bikes 45 km.
Each training day, Ann increases her biking distance by 3% compared to the day before,
while Bob increases his biking distance by 3 km compared to the day before.
(a) Write out the formula in terms of n for the distance An that Ann rides on the nth day
of her training.
ANSWER:An =
(b) Write out the formula in terms of n for the distance Bn that Bob rides on the nth day
of his training.
ANSWER:Bn =
31st
(c) On the
day of their training, who bikes farther, Ann or Bob, and by how many
kilometers?
ANSWER:
bikes farther than
by
km.
(d) What is the total distance that Bob biked during his entire training month? (that is,
what is the sum of the distances he biked in day 1, plus in day 2, ... , plus in day 31?)
ANSWER:
kilometers.
Math 111
Final Exam
Winter 2013
7. (16 points)
(a) If you want to earn 15% annual simple interest on an investment, how much should you
pay for a note that will be worth $6,750 in 10 months?
ANSWER: $
(b) A certain type of bacteria culture triples every two hours. The initial culture contains
1,000 bacteria. How many bacteria are in the culture after 11 hours?
ANSWER:
bacteria
(c) You invest $1,000 in a mutual fund that depreciates by 2.5% per year. That is, the
investment loses 2.5% of its value each year. When will the value of your investment
be $900?
ANSWER: after
years
(d) You buy an apartment for $175,000 and you sell it after 3 years for $210,000. What was
your annual rate of return (compounded annually)?
ANSWER: r × 100% =
%
Math 111
Final Exam
Winter 2013
8. (12 points)
(a) A man makes $3,000 contributions at the end of each half-year to a retirement account
for a period of 8 years. The account earns 4.2%, compounded semiannually. For the next
10 years, he makes no additional contributions and no withdrawals. Find the balance of
the account after the 18 years.
CIRCLE ONE:
Ordinary Annuity
Annuity Due
ANSWER: $
(b) Jack has $70,000 in an account which earns 4%, compounded annually. If he withdraws
$5,000 from this account at the beginning of each year, how long until he runs out of
money in the account? Round your answer to the nearest year.
CIRCLE ONE:
Ordinary Annuity
Annuity Due
ANSWER: After
years.
(c) A woman paid $5,000 down for a car and agreed to make payments of $330 at the end
of each month, for 36 months. If money is worth 3%, compounded monthly, how much
would the car have cost if she had paid cash?
CIRCLE ONE:
Ordinary Annuity
Annuity Due
ANSWER: $