Question 1
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B0/10 pts 5 3 399 0 Details
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WolframAlpha is convenient to plug several successive inputs in one
complicated function. For example, type "X^2y^22xy for x=1 where y=4"
in Wolfram Alpha ", then change the values of x and y as many times as
you want.
Find the critical point of the function
f(x, y) = 1 – 4x – 6x2 – 5y – 2y2
This critical point is a v Select an answer
Maximum
Question Help: Vi
Minimum
Saddle
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Question
<
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B0/10 pts 53 99 0 Details
Suppose that f(x, y) = x4 + y4 – xy
Then the minimum value is
Gda
Question 3
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B0/10 pts 5 3 99 0 Details
Find and classify the critical points of z =
(z– 6x) (y2 – 3y)
Local maximums at:
Local minimums at:
Saddle points at:
For each of the fields above, enter an ordered pair (x, y) (or a comma
separated list of ordered pairs) where the max/min/saddle occurs. If
there are none enter DNE.
Question 4
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B0/10 pts 5 3 399 0 Details
A company manufactures 2 models of MP3 players. Let x represent the
number (in millions) of the first model made, and let y represent the
number (in millions) of the second model made.
The company's revenue can be modeled by the equation
R(x, y)
60x + 1307 – 3x2 – 2y2 – xy
Find the marginal revenue equations
R (x, y) =
C
R, (2, y) =
We can achieve maximum revenue when both partial derivatives are
equal to zero. Set Rx
O and Ry O and solve as a system of
equations to the find the production levels that will maximize revenue.
=
Revenue will be maximized when:
X =
y =
Nuortion Voln
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Question 5
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B0/10 pts 53 99 0 Details
An opentop rectangular box is being constructed to hold a volume of 150
in?. The base of the box is made from a material costing 8 cents/in?. The
front of the box must be decorated, and will cost 11 cents/in2. The
remainder of the sides will cost 3 cents/in?.
Find the dimensions that will minimize the cost of constructing this box.
Front width:
in.
Depth:
in.
Height:
in.
7:35
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Find the power series for f(x) = ln(1 – x4) centered at x = 0 from the known power series expansion
In(1+2) = Į ( 1)+1.x
+lxn
n
n=1
f(x) = À
n=1
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Differentiate the given series expansion of f termbyterm to obtain the corresponding series expansion
for the derivative of f.
6n
1
126
Σ
If f(x) =
n=0
f'(x) =
= 8
n=1
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x2
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cos(x)  1
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We know that the MacLaurin series of cos(x) is 1
Replace cos(x) with these first three terms to find lim
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x2
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4!
cos(x)  1
22
2 +0
We know that the MacLaurin series of cos(x) is 1
Replace cos(x) with these first three terms to find lim
5
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The student council is hosting a drawing to raise money for scholarships. They are selling tickets for $9
each and will sell 600 tickets. There is one $1,000 grand prize, two $200 second prizes, and sixteen $30
third prizes. You just bought a ticket. Find the expected value for your profit. Round to the nearest cent.
$
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An LG Dishwasher, which costs $850, has a 24% chance of needing to be replaced in the first 2 years of
purchase. A twoyear extended warranty costs $112.10 on a dishwasher.
a) Write out the probability distribution for the value of the extended warranty. The value, denoted X
below, is the money paid by the warranty to the customer, minus the cost of the warranty.
Make sure you enter your X values from smallest to largest.
Х
P(X)
b) What is the expected value of the extended warranty?
Round final answer to 2 decimal places and write the units in the second box.
c) Which of the following is the correct interpretation of the expected value of the warranty?
✓ Select an answer
For a large number extended warranties bought by customers, the average gain is 91.9 dollars per warranty
Every time you buy such a warranty you will gain 91.9 dollars
Every time you buy the extended warranty the dishwasher breaks
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Dandelions are studied for their effects on crop production and lawn growth. In one region, the mean
number of dandelions per square meter was found to be 5.
Find the probability of no dandelions in an area of 1 m2. Give at least four decimals.
P(X = 0) =
Find the probability of at least one dandelion in an area of 1 m2. Give at least four decimals.
Plat least one) =
Find the probability of at most two dandelions in an area of 1 m2. Give at least four decimals.
P(X < 2) =
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Question 7
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77% of a basketball player's free throw shots are successful. In a given game, find the probability that
(a) her first successful freethrow shot is shot number five.
(b) she makes her first successful freethrow within the first four shots.
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Suppose that the distance, in miles, that people are willing to commute to work is an exponential random
variable with mean 25 miles.
(a) What percentage of people are willing to commute at most 42 miles to work?
(b) 55% of people are willing to commute at most how many miles to work?
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Question 9
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Private nonprofit fouryear colleges charge, on average, $26,610 per year in tuition and fees. The standard
deviation is $7,338. Assume the distribution is normal. Let X be the cost for a randomly selected college.
Round all answers to 4 decimal places where possible.
a. What is the distribution of X? X  NO
(Round to the nearest dollar.)
b. Find the probability that a randomly selected Private nonprofit fouryear college will cost less than
24,402 per year.
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c. Find the 79th percentile for this distribution. $
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The lifetime of a printer costing $130 is exponentially distributed with mean 3.67 years. The manufacturer
agrees to pay a full refund to a buyer if the printer fails during the first half year following its purchase and
a onehalf refund if it fails during the second half year.
If the manufacturer sells 240 printers, how much should it expect to pay in refunds?
S
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Identify the equation of the plane shown below:
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Find the distance from the point (4,5,6) to the yzplane.
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Match each contour map with its graph
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A contour map for a function f is shown. If you start at the point (4,7) and move in the positive x
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40
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Quiz: Test 4 Part 1 (Online
marin.instructure.com/courses/17246/assignments/148827
At an Oregon fibermanufacturing facility, an analyst estimates that the weekly number of pounds of
acetate fibers that can be produced is given by the function:
z = f(x, y) = 12000x + 4500y + 10x²y  14x3
Where:
z = the weekly # of pounds of acetate fiber
x = the # of skilled workers at the plant
y = the # of unskilled workers at the plant
Determine the following:
A) The weekly number of pounds of fiber that can be produced with 16 skilled workers and 33 unskilled
workers.
pounds
Answer =
B) Find an expression (fc) for the rate of change of output with respect to the number of skilled workers.
Answer = fo =
C) Find an expression (fy) for the rate of change of output with respect to the number of unskilled
workers.
Answer = fy =
D) Find the rate of change of output with respect to skilled workers when 16 skilled workers and 33
unskilled workers are employed. (Your answer will be a number.)
weekly pounds per skilled worker
Answer =
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E) Find the rate of change of output with respect to unskilled workers when 16 skilled workers and 33
unskilled workers are employed. (Your answer will be a number.)
A
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Question 18
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I P(L,K) = 30L0.9600.1
Consider the CobbDouglas Production function:
Find the marginal productivity of labor and marginal productivity of capital functions. Enter your answers
using CAPITAL L and K, or your answer will not be recognized.
PL
PK =
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