Question

a) The Cost of selling widgets is given by the cost function c(x)= 4x+10.

The price of each widget is given by the function p= 50-0.05x.

A) How many widgets must be sold to maximize profit?

B) What will be the Maximum Profit?

C) What price per widget must be charged in order to maximize
profit.

Answer #1

A company produces x widgets for a cost of C(x) dollars and
sells them for 2280 dollars per widget.
If the cost function is C(x)=6450+760x+0.8x2, find the production
level that will maximize profit.
x = _____widgets
Be sure to apply a test to check that you have found the
maximum.

?Raggs, Ltd. a clothing? firm, determines that in order to sell
x? suits, the price per suit must be p=180?0.75x. It also
determines that the total cost of producing x suits is given by
C(x)=4000+0.75x^2.
?a) Find the total? revenue,
R(x)=
?b) Find the total? profit,
P(x)=
?c) How many suits must the company produce and
sell in order to maximize? profit?
?d) What is the maximum? profit?
?e) What price per suit must be charged in
order to maximize?...

The cost of producing a plastic toy is given by the function
C(x) = 8x + 25, where x is the number of hundreds of toys. The
revenue from toy sales is given by R(x) = −x2 + 120x − 360. Since
profit = revenue − cost, the profit function must be P(x) = −x2 +
112x − 385 (verify). How many toys sold will produce the maximum
profit? What is the maximum profit?

A company making widgets has a price-demand equation p(x) = 400
− .02x where x is the monthly demand and p is the price per widget
and the cost equation is C(x) = 200x + 20, 000. Find the price that
maximizes the profit and give the maximum profit.

A video game console manufacturer determines that in order to
sell x units of a new console, the price per unit, in dollars, must
be p=1750-2x . The manufacturer also determines that the total cost
of producing x units is given by (Cx)=22500+15x . Find the total
revenue function R(x) ? Find the total profit function P(x) ? How
many units must the company produce and sell in order to maximize
profit? (Use the second derivative test to verify this...

Let's say an online retailer sells tablets. The demand (price)
function is given by p(x)=500−18x, where x is the number of tablets
produced sold and p(x) is the price per week, while the cost, in
dollars per week to produce x tablets is given by C(x)=35000+120x.
Based on this, answer the following questions:
1. Determine the Revenue Function.
2. Determine the number of tablets the retailer would have to
sell to maximize revenue. What is the maximum revenue?
3. Determine...

The revenue and cost functions for a particular product are
given below. The cost and revenue are given in dollars, and
x represents the number of units .
R(x) = −0.2x2 + 146x
C(x) = 66x + 7980
(a) How many items must be sold to maximize the revenue?
(b) What is the maximum revenue?
(c) Find the profit function.
P(x) =
−.2x2+212x+7980
(d) How many items must be sold to maximize the profit?
(e) What is the maximum profit?...

Widget Makers is a startup selling widgets. Each widget sells
for $10 and costs $7 to make. The company’s annual overhead
expenses (salaries, rent, insurance, and marketing) is $400,000.
How many widgets per year does it have to sell to break even?
If Widget makers sold 40,000 widgets in the year that just ended
and sales will grow at 30% per year, then how many months will it
take to break even?

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...

retired potter can produce pitchers at a cost of $5 each. He
estimates his price function to be
p = 19 − 0.5x,
where p is the price at which exactly x
pitchers will be sold per week. Find the number of pitchers that he
should produce and the price that he should charge in order to
maximize profit. Also find the maximum profit.
quantity
pitchers
price
$
profit
$

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