Question

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 Profit Function.

4. Determine the number of tablets the retailer would have to sell to maximize profit. What would the maximum profit be?

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

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?

JMC manufacturers sells 500 units per week at 29 dollars per
unit. If the price is reduced by one dollar, 20 more units will be
sold. In addition, the cost function for JMC Manufacturers is also
given by ?(?) = 40? + 10000
a. To maximize the revenue, find the following:
I. [2 marks]. The number of units sold number of units sold.
II. [2 marks]. The maximum revenue.
b. [2 marks]. Find the value of x that maximizes the...

The demand function for sunshades is given as:
?=270−2?P=270−2Q
where P is the price paid for a sunshade and Q
is the number of sunshades demanded.
The fixed cost is 460 while the cost per shade is 70.
When profit is maximised, the number of sunshades sold
=Answer
The maximum profit = Answer
When profit is maximised the marginal revenue, MR = Answer
When profit is maximised the marginal cost, MC = Answer

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 cost function C and the price-demand function
p are given. Assume that the value of
C(x)
and
p(x)
are in dollars. Complete the following.
C(x) =
x2
100
+ 7x + 3000;
p(x) = −
x
40
+ 5
(a) Determine the revenue function R and the profit
function P.
R(x)
=
P(x)
=
(b) Determine the marginal cost function MC and the
marginal profit function MP.
MC(x)
=
MP(x)
=
Here is a picture of the problem:
https://gyazo.com/b194ec1a9b7787b8b81ad12388ff915e

Let’s say we have a market demand curve given by the following
equation:
q=10000-200p
Let’s say we need to maximize the profit:
So we have revenue function f(p) and cost function given by
1p
So profit, pi(p) = f(p) + pq
We can find the value of p at which this can be maximum by
differentiating pi(p) and making it equal to zero. To find whether
it is maximum value , we again do the derivative and check whether
it...

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.

* City Computers has determined that the price-demand and
revenue functions are given by p(x) = 2,000 – 6x and
R(x) = x(2,000 – 6x), where x is in thousands of computers.
This means that R(x) is measured in thousands of dollars.
Additionally we know:
* The fixed cost is $100,000.
* The variable cost is $250 per computer.
This means that the cost function is given by C(x) = 100 +
250x. Also again C(x) is measured in thousands...

The demand function for a Christmas music CD is given by
q=0.25(225−p^2)
where q (measured in units of a hundred) is the quantity
demanded per week and pp is the unit price in dollars.
(a) Evaluate the elasticity at p=10. E(10)=
(b) Should the unit price be lowered slightly from 10 in order to
increase revenue?
yes no
(c) When is the demand unit
elastic? p=______dollars
(d) Find the maximum revenue. Maximum revenue =________ hundreds of
dollars

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