Question

1. When $x thousand is spent on advertising a product, the sales (number of units sold) is given by S(x)= -x^3+9x^2+21x+100 for 0<=x<=10. Which of the following is not correct? Optional Answers:

1. Sales has a global (absolute) minimum at x=0

2. Sales has a global (absolute) maximum at x=7

3. Rate of sales has a global (absolute) maximum at x=3

4. Rate of sales has a global (absolute) minimum at x=0

Answer #1

A company estimates that it will sell N(x)units of a
product after spending $x thousand on advertising, as
given by: N(x) = -0.25x^4 + 13x^3 - 180x^2 + 10,000. 15<x<24
When is the rate of change of sales increasing and when is it
decreasing?
What is the point of diminishing returns and the maximum rate of
change of sales?

A company estimates that if x thousand cedis is spent
on the marketing of a certain product, Q(x)
thousand units of the product will be sold, where Q(x) = 7x
27 + x
2
.
(a) Determine the domain of the function defined. [2 Marks]
(b) Determine how much of the product will be sold if the company
does not spend any money on
marketing. [2 Marks]
(c) Determine the amount of money the company must spend on
marketing to...

The data below represent a firm’s dollars spent on advertising
for a sample of 4 months and the firm’s sales (in units sold) for
those months.
Month
Advertising Expenditures (x)
Units Sold (y)
1
$2,215
543
2
$2,975
664
3
$2,150
538
4
$2,060
575
1. What is the slope of the simple regression line (using the
OLS method)?
2. What is the intercept of the simple regression line (using
the OLS method)?
3. What is the correct interpretation of...

Suppose that a company's sales volume y (in thousands
of units) is related to its advertising expenditures x (in
thousands of dollars) according to the following.
xy − 48x + 16y = 0
Find the rate of change of sales volume with respect to
advertising expenditures when
x = 16
(thousand dollars).

1.Based on the equation Y = 4.29 + 143.3X, Sales(Y) is in Units
of $1000.00 and Advertising(X) is in Units of $100. What are Sales
when $2,140.00 is spent on advertising?
2. Sales(Y) is in Units of $1000.00 and Advertising(X) is in
Units of $100. If we want to calculate the value of sales when
$40,614.00 is spent on advertising. What do we use for X in the
following equation? Y=42.9+143.3X.
Please, do the two questions and show processes

A marine manufacturer will sell N(x) power boats after spending
$x thousand on advertising is given by N(x)=1000-(3780/x) for
5≤x≤30
Find N'(x) with appropriate units. Explain what the first
derivative means in this situation. (By hand )
Find the number of power boats sold and the instantaneous
rate of sales after spending $9,000 on advertising. Write a brief
explanation of these results.
Use a table of values to sketch a well labelled graph of this
function between $5,000 and $30,000....

The weekly demand function for x units of a product
sold by only one firm is p = 400 − 1/2x dollars, and the average
cost of production and sale is
C = 100 + 2x dollars.
(a) Find the quantity that will maximize profit.
units
(b) Find the selling price at this optimal quantity.
$ per unit
(c) What is the maximum profit?
$
The weekly demand function for x units of a product sold by only
one firm is...

Let f(x)=4x(^3)-9x(^2)+6x-1 Find:
a.) absolute minimum of f(x) on the interval [0,1].
b.) absolute maximum of f(x) on the interval [0,1].

Saltwater taffy can be sold wholesale for $45 per thousand
individual candies. The cost of producing x thousand candies is
?(?) = .001?3 + .045?2 − 1.75?
c. Find the marginal revenue equation. Interpret its meaning
d. Find the marginal profit equation
e. What number of candies will produce a marginal profit of
$0?
f. Does the value from part e give a maximum or minimum? Verify
your answer.
g. Find the maximum or minimum profit

The monthly demand function for x units of a product
sold by a monopoly is
p = 6,100 −
1/2x2 and its average cost
is C = 3,030 + 2x dollars. Production is
limited to 100 units.
a) Find the profit function, P(x), in dollars.
b) Find the number of units that maximizes profits. (Round your
answer to the nearest whole number.)
c) Find the maximum profit. (Round your answer to the nearest
cent.)

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