Midterm 2
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School
University of Ottawa *
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Course
1305
Subject
Aerospace Engineering
Date
Dec 6, 2023
Type
Pages
6
Uploaded by MateMosquitoPerson716
ADM1305C
–
Fall 2023
Second Midterm
•
You are allotted 80 minutes to complete your midterm examination. Following that, you will have an
extra 10 minutes to submit your exam on Brightspace. Please note that this is a closed-book exam.
•
You are permitted to use
only
the provided formula sheet
or
your personal double-sided formula
sheet with relevant notes during the examination.
•
A non-programmable calculator is mandatory for this exam.
•
Full credit will only be awarded for clearly documented calculations and comprehensible
explanations of your results. These components significantly impact your final grade.
Marking scheme
Question 1
Question 2
Question 3
Question 4
Question 5
Total
/25
/25
/25
/25
/25
/100
Statement of Personal Ethics Regarding Examinations at Telfer School of Management
Individual Exam: By signing this Statement, I am attesting to the fact that I have adhered to the fraud
policies outlined in the Academic Regulations in the University’s Undergraduate Studies Calendar
(Academic Fraud Webpage).
______________________________
__________________________
Last Name, First Name (print)
Student Number
_____________________________
__________________________
Professor’s Name
Course Code and Section
Select and thoroughly answer any four out of the following five questions.
1.
(25 Points) Laura, the coordinator of a music festival, predicts that if she advertises the festival x days
before it occurs, the expected income will be R(x) thousand dollars, where:
The expenses for promoting the festival for x days amount to C(x) thousand dollars, where:
a.
Develop the profit function.
b.
Determine the ideal number of days Laura should promote the festival in advance to maximize
her profit. Also, calculate the maximum profit and show that this point is indeed a maximum.
c.
Write the expression for the ratio of income to expenses and analyze the behavior of this ratio as
x approaches 0.
d.
Explore how the ratio of income to expenses changes as x approaches infinity.
2.
(25 Points) Jordan, the director of a local library, has found that when x% of the library's resources
are in use, the total operating expense is C(x) hundred dollars, where:
C x
( )
=
8
x
2
-
636
x
-
320
x
2
-
68
x
-
960
The library aims to maximize resource utilization while maintaining efficient operations, targeting
approximately 80% usage of its resources.
a.
What cost should Jordan expect when the library is operating at this ideal capacity?
b.
Find the critical points of C(x). Determine these points and discuss their significance in the
context of managing the library's resources and operating expenses.
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3.
(25 Points) Imagine you're on a mountain expedition where the ambient air temperature is a chilly
30°F. The perceived temperature, or 'feels-like' temperature, experienced by climbers is influenced by
the wind speed at altitude v miles per hour (mph). This relationship can be modeled by:
a.
Calculate the 'feels-like' temperature when the wind speed is 20 mph and again at 50 mph.
b.
Determine the wind speed required to produce a 'feels-like' temperature of 0°F on this mountain.
c.
Evaluate the continuity of the 'feels-like' temperature function at wind speeds of 4 mph and 45
mph. Is the function continuous at these points?
4.
(25 Points) The owner of a boutique winery predicts that producing 400 bottles of a premium wine
will cost $10,000 one year from now, and each bottle can be sold for $30 at that time. She also
anticipates that in one year, the selling price per bottle will increase by 75 cents per month, while the
production rate will decrease by 2 bottles per month, and the production cost will remain constant.
a.
If x represents the number of wine bottles produced at time t, where t = 0 corresponds to one year
from now, define the profit function P(x). Calculate the rate at which profit P(x) will be changing
one year from now with respect to x. Based on your calculation, determine whether the profit will
be increasing or decreasing at that time.
b.
Analyze the rate at which the average profit per bottle will be changing one year from now. Will
the average profit per bottle be increasing or decreasing at that time?
5.
(25 Points) The market value
V
(in thousands of dollars) of a high-end sports car is known to
depreciate over time. The rate of depreciation depends on the car's usage, measured in the number of
miles
N
driven per day. The relationship between the car's value and its daily mileage is given by:
Meanwhile, the car's daily mileage
N
itself, changes over time and is described as a function of
t
,
where
t
represents the number of months since the car was purchased:
Determine the rate at which the value of the sports car is changing with respect to time 9 months from
the purchase date. Based on your calculations, conclude whether the value of the car will be
increasing or decreasing at that time.
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