Question

The demand for cat food is given by

D(x)=110e^−0.02x

where x is the number of units sold and D(x) is the price in
dollars.

Find the revenue function.

R(x)=

Find the number of units sold that will maximize the revenue.

Select an answer units or dollars

Find the price that will yield the maximum revenue.

Select an answer units or dollars

Answer #1

The demand function for a particular brand of LCD TV is given
by
p = 2400 − 30x
where p is the price per unit in dollars when
x television sets are sold.
(a) Find the revenue function.
R(x) =
(b) Determine the number of sets that must be sold in order to
maximize the revenue.
sets
(c) What is the maximum revenue?
$
(d) What is the price per unit when the revenue is maximized?
$ per unit

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...

Total revenue is in dollars and x is the number of
units.
Suppose that in a monopoly market, the demand function for a
product is given by
p = 450 − 0.1x
where x is the number of units and p is the
price in dollars.
(a) Find the total revenue from the sale of 500 units.
$
(b) Find the marginal revenue MR at 500 units.
MR = $
Interpret this value.
The 501st unit will lose |MR| dollars...

3. As the number of units sold increases, market price decreases
(supply and demand).
Suppose that p = 5000 – 0.75x , where p
is the market price and x is the number of
units sold. Suppose further that the
cost of producing x items is given by
C(x) = 3000 + 15x, and that the revenue
from the sale of x units is given by
R(x) = 120x.
a. Express the cost as a...

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...

Total revenue is in dollars and x is the number of units.
Suppose that in a monopoly market, the demand function for a
product is given by the following equation, where x is the number
of units and p is the price in dollars. p = 370 − 0.3x (a) Find the
total revenue from the sale of 500 units. $ (b) Find the marginal
revenue at 500 units. $ (c) Is more revenue expected from the 501st
unit sold...

The demand function for a Christmas music CD is given by
q=D(p)=0.25(225−p2)where q (measured in units of a hundred) is the
quantity demanded per week and p is the unit price in dollars. (a)
Find the elasticity function E(p)= _________
(b) Evaluate the elasticity at 10. E(10)= ________
(c) Should the unit price be lowered slightly from 10 in order
to increase revenue? Yes or No.
(d) Use the elasticity of demand to find the price which
maximizes revenue for...

1) For a company the demand equation is given by p = 100 -
0.025x, where p represents the price per unit when x quantity of
units is sold. Determine the marginal revenue when 2,500 units are
sold, that is, R ’(2,500) and interpret the result.
2) The total weekly cost in dollars for manufacturing x
calculators in a company is given by the function C (x) = 10x +
2,500. Determine the marginal average cost function.

The demand for tickets to an amusement park is given by
p=70−0.04q, where p is the price of a ticket in dollars and q is
the number of people attending at that price.
(a) What price generates an attendance of 1500
people? What is the total revenue at that price? What is the total
revenue if the price is $20?
(b) Write the revenue function as a function of
attendance, q, at the amusement park. Use the multiplication sign
in...

The demand for a product is D(x)=75-0.3x where x is the price in
dollars.
At a price of $100, what is the elasticity of demand and explain
whether it is elastic or inelastic?
Determine the prices for which the demand is elastic?
Find the maximum revenue?

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