Use the profit equation from matched problem 3 : P x = R x − C x = − 5 x 2 + 75.1 x − 156 Profit function domain : 1 ≤ x ≤ 15 (a) Sketch a graph of the profit function in a rectangular coordinate system . (b) Break even points occur when P x = 0 find the break-even points algebraically to the nearest thousand cameras (c) Plot the profit function in an appropriate viewing window. (d) Find the break-even point graphically to the nearest thousand cameras. (e) A loss occurs if P x < 0 , and a profit occurs if P x > 0 for what values of x (to the nearest thousand cameras) will a loss occur? A profit?
Use the profit equation from matched problem 3 : P x = R x − C x = − 5 x 2 + 75.1 x − 156 Profit function domain : 1 ≤ x ≤ 15 (a) Sketch a graph of the profit function in a rectangular coordinate system . (b) Break even points occur when P x = 0 find the break-even points algebraically to the nearest thousand cameras (c) Plot the profit function in an appropriate viewing window. (d) Find the break-even point graphically to the nearest thousand cameras. (e) A loss occurs if P x < 0 , and a profit occurs if P x > 0 for what values of x (to the nearest thousand cameras) will a loss occur? A profit?
P
x
=
R
x
−
C
x
=
−
5
x
2
+
75.1
x
−
156
Profit function
domain
:
1
≤
x
≤
15
(a) Sketch a graph of the profit function in a rectangular coordinate system.
(b) Break even points occur when
P
x
=
0
find the break-even points algebraically to the nearest thousand cameras
(c) Plot the profit function in an appropriate viewing window.
(d) Find the break-even point graphically to the nearest thousand cameras.
(e) A loss occurs if
P
x
<
0
, and a profit occurs if
P
x
>
0
for what values of
x
(to the nearest thousand cameras) will a loss occur? A profit?
Formula Formula A polynomial with degree 2 is called a quadratic polynomial. A quadratic equation can be simplified to the standard form: ax² + bx + c = 0 Where, a ≠ 0. A, b, c are coefficients. c is also called "constant". 'x' is the unknown quantity
Consider the ceocomp dataset of compensation information for the CEO’s of 100 U.S. companies. We wish to fit aregression model to assess the relationship between CEO compensation in thousands of dollars (includes salary andbonus, but not stock gains) and the following variates:AGE: The CEOs age, in yearsEDUCATN: The CEO’s education level (1 = no college degree; 2 = college/undergrad. degree; 3 = grad. degree)BACKGRD: Background type(1= banking/financial; 2 = sales/marketing; 3 = technical; 4 = legal; 5 = other)TENURE: Number of years employed by the firmEXPER: Number of years as the firm CEOSALES: Sales revenues, in millions of dollarsVAL: Market value of the CEO's stock, in natural logarithm unitsPCNTOWN: Percentage of firm's market value owned by the CEOPROF: Profits of the firm, before taxes, in millions of dollars1) Create a scatterplot matrix for this dataset. Briefly comment on the observed relationships between compensationand the other variates.Note that companies with negative…
6 (Model Selection, Estimation and Prediction of GARCH) Consider the daily returns rt
of General Electric Company stock (ticker: "GE") from "2021-01-01" to "2024-03-31",
comprising a total of 813 daily returns. Using the "fGarch" package of R, outputs of
fitting three GARCH models to the returns are given at the end of this question.
Model 1 ARCH (1) with standard normal innovations;
Model 2
Model 3
GARCH (1, 1) with Student-t innovations;
GARCH (2, 2) with Student-t innovations;
Based on the outputs, answer the following questions.
(a) What can be inferred from the Standardized Residual Tests conducted on Model 1?
(b) Which model do you recommend for prediction between Model 2 and Model 3?
Why?
(c) Write down the fitted model for the model that you recommended in Part (b).
(d) Using the model recommended in Part (b), predict the conditional volatility in the
next trading day, specifically trading day 814.
4 (MLE of ARCH) Suppose rt follows ARCH(2) with E(rt) = 0,
rt = ut, ut =
στει, σε
where {+} is a sequence of independent and identically distributed (iid) standard normal
random variables.
With observations r₁,...,, write down the log-likelihood function for the model esti-
mation.
Chapter 2 Solutions
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
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