Question

A manufacturer of bicycle helmets estimates that the monthly cost to produce q helmets is ?(?) = 6200 + 7.3? + 0.002?^2 dollars and the expected revenue, in dollars, is ?(?) = 31? − 0.003?^2. Find the number of helmets that should be produced each month in order to maximize profit, and find the maximum profit.

Answer #1

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
$

a) Find the values of x and y in order to maximize the value of
Q.
2x+y=10
3x^2y=Q
b) Find the number of units you will have to produce if you want
to
maximize profit if the cost and price equations are given below.
Then find the maximum
profit made. (6 points)
C(x)= 4x+10
R(x)= 50x-0.5x^2
Units Produced: ____________________
Maximum Profit: ____________________
(Please show all work possible)

A manufacturer estimates that when q thousand units of a
particular commodity are produced each month, the total cost will
be C(q) =0.4q 2 +3q+40 thousand dollars, and all q units can be
sold at a price of p(q)= 22.2 - 1.2q dollars per unit. At what
level is the average cost per unit minimized?
a)10 thousand
b)17.6 thousand
c)9 thousand
d)6 thousand

A manufacturer estimates that its product can be produced at a
total cost of C(x) = 45000 + 150x + x 3 dollars If the manufacturer
sells the product for $4600 per unit, determine the level of
production x, that will maximize the profit. Round your answer to
the nearest tenth of a unit. Use calculus to support your answer.
Box both your profit function and your final answer.

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...

1. A tire manufacturer estimates that q thousand radial
tires will be purchase by wholesalers when the price is D ( q ) = −
0.1 q 2 + 90 dollars per time and the same number of tires will be
supplied when the price is S ( q ) = 0.2 q 2 + 50.
a. Find the equilibrium price and the the quantity supplied and
demanded at that price.
b. Determine the consumers' and producers' surplus at the...

Q1- A manufacturer estimates that its variable cost for
manufacturing a product is given by the following expression: C(q)
= 25q 2 + 2000q [$] where C is the total cost and q is the quantity
produced. Derive expressions for the revenue and the profit,
substitute if q=10
Q2- Economists estimate that the supply function and demand
function for the widget market is given by the following
expressions: q = 0.2 · π − 40 π = −10q + 2000...

Suppose the Sunglasses Hut Company has a profit function given
by P(q)=-0.01q2+4q-26, where q is the number of thousands of pairs
of sunglasses sold and produced, and P(q) is the total profit, in
thousands of dollars, from selling and producing q pairs of
sunglasses.
A) Find a simplified expression for the marginal profit function.
(Be sure to use the proper variable in your answer.)
Answer: MP(q)=
B) How many pairs of sunglasses (in thousands) should be sold to
maximize profits?...

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...

Unendo, is a large computer game
manufacturer.
They have estimated that the demand
function for their game "Call of Duty:WWIII" is as
follows ...
p = 89 - 0.05q;
where p is the price of a game and q
is the number of game produced and sold per week.
They estimate that their cost function in
dollars is ...
C(q) = 25q + 5000;
where the fixed cost is $5000 and the marginal cost is
$25 per game
Unendo wishes...

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