Question

A one-product company finds that its profit, P, in millions of dollars, is given by the following equation where a is the amount spent on advertising, in millions of dollars, and p is the price charged per item of the product, in dollars.

P(a,p)=4 ap + 50 p - 9 p^2 - one tenth a^2 p - 90

Find the maximum value of P and the values of a and p at which it is attained. The maximum value of P is attained when a is $ -------- million and p is $ -------?. The maximum value of P is $ ------- million.?

Answer #1

The profit P (in thousands of dollars) for a company spending an
amount s (in thousands of dollars) on advertising is given by the
following equation. P = − 1/10s^3 + 3s^2 + 600. Find the amount of
money the company should spend on advertising in order to yield a
maximum profit. Also, Find the point of diminishing returns.

Listed below are paired data consisting of amounts spent on
advertising (in millions of dollars) and the profits (in millions
of dollars). Determine if there is a significant negative linear
correlation between advertising cost and profit . Use a
significance level of 0.01 and round all values to 4 decimal
places.
Advertising Cost
Profit
3
14
4
14
5
25
6
22
7
27
8
18
9
33
10
26
11
36
12
22
Ho: ρ = 0
Ha: ρ...

The profit P (in thousands of dollars) for a company
spending an amount s (in thousands of dollars) on
advertising is shown below.
P = −1/3 s3 + 9s2 + 400
(a) Find the amount of money the company should spend on
advertising in order to yield a maximum profit.
s = thousands of dollars (b) The
point of diminishing returns is the point at which the
rate of growth of the profit function begins to decline. Find the
point of...

Assume that a monopolist sells a product with inverse demand
given by p = 12 – 0.5q,
where p is the price of the product
and q is its quantity, and the monopolist’s
marginal and average cost is equal to 6.
(a) Find the profit maximising level of q and
p, and the firm’s profit. Find the profit maximising level
of output and profit if the maximum price that can be charged per
unit is (i) p = 7, (ii) p = 10.
(b)...

Question 5
Assume that a monopolist sells a product with inverse demand
given by p = 12 – 0.5q,
where p is the price of the product
and q is its quantity, and the monopolist’s
marginal and average cost is equal to 6.
(a) Find the profit maximising level of q and
p, and the firm’s profit. Find the profit maximising level
of output and profit if the maximum price that can be charged per
unit is (i) p = 7, (ii) p =...

Assume that a monopolist sells a product with inverse demand
given by p = 12 – 0.5q, where p is the price of the product and q
is its quantity, and the monopolist’s marginal and average cost is
equal to 6. Word limit per question: 400 words (200 words per part
of question)
(a) Find the profit maximising level of q and p, and the firm’s
profit. Find the profit maximising level of output and profit if
the maximum price...

An electronic company’s profit from selling x thousands of one
product and y thousands of another is given by the formula in units
of thousands of dollars:
P(x,y)=−2x2 +5xy−4y2 +7x+7y+200.
• Show that the profit P is maximized only at the point (x, y) =
(13, 9) and determine the maximum profit.
• Using an appropriate differential determine approximately the
profit lost if x is only 12.7 and y only 8.6.

1) Suppose the cost in dollars of manufacturing q item is given
by: C= 2000q + 3500
and the demand equation is given by: q= sqrt(15,000-1.5p)
in terms of the demand q,
a) find an expression for the revenue R
b) find an expression for the profit P
c) find an expression for the marginal profit
d) Determine the value of the marginal profit when the price is
$5000
2) A manufacturer sells video games with the following cost and...

5.) A computer software company models the profit on its lastest
video game using the relation
p(x) = -4x^2+20x-9
where x is the number ofgames produced in hundred thousand and
p(x) is the profit in millions of dollars.
a) what is the profit when 500000 games are produced?
b) what type of function is p(x)
c.) what are the best break even points for the company?(Hint:
when profit is 0.)

A company is trying to maximize its profit on the sale of items
A, B, and C. They make a profit of 60 dollars on each item of type
A, 25 dollars on each item of type B, and $50 on each item of type
C. Each product requires polishing and assembling time. Type A
items requre 4 minutes of polishing, type B items require 3 minutes
of polishing, and type C items require 5 minutes of polishing. Type
A...

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