Question

Maximizing Profits A manufacturer of tennis rackets finds that the total cost C(x) (in dollars) of...

Maximizing Profits

A manufacturer of tennis rackets finds that the total cost C(x) (in dollars) of manufacturing x rackets/day is given by

C(x) = 500 + 7x + 0.0003x2.

Each racket can be sold at a price of p dollars, where p is related to x by the demand equation

p = 10 − 0.0002x.

If all rackets that are manufactured can be sold, find the daily level of production that will yield a maximum profit for the manufacturer. Hint: The revenue is

R(x) = px,

and the profit is

P(x) = R(x) − C(x).

rackets=

Math   Precalculus   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Maximizing Profits The quantity demanded each month of the Walter Serkin recording of Beethoven's Moonlight Sonata,...
Maximizing Profits The quantity demanded each month of the Walter Serkin recording of Beethoven's Moonlight Sonata, produced by Phonola Media, is related to the price per compact disc. The equation p = −0.00042x + 9 (0 ≤ x ≤ 12,000) where p denotes the unit price in dollars and x is the number of discs demanded, relates the demand to the price. The total monthly cost (in dollars) for pressing and packaging x copies of this classical recording is given...
A manufacturer finds that the revenue generated by selling x units of a certain commodity is...
A manufacturer finds that the revenue generated by selling x units of a certain commodity is given by the function R(x) = 80x − 0.5x2, where the revenue R(x) is measured in dollars. What is the maximum revenue, and how many units should be manufactured to obtain this maximum? $ _______, at ______units
1) Suppose the cost in dollars of manufacturing q item is given by: C= 2000q +...
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...
Acrosonic's production department estimates that the total cost (in dollars) incurred in manufacturing x ElectroStat speaker...
Acrosonic's production department estimates that the total cost (in dollars) incurred in manufacturing x ElectroStat speaker systems in the first year of production will be represented by the following function, where R(x) is the revenue function in dollars and x denotes the quantity demanded. Find the following functions (in dollars) and compute the values (in dollars). C(x) = 110x + 27,000    and    R(x) = −0.04x2 + 800x (a)Find the profit function P. (b)Find the marginal profit function P '. (c)Compute the following...
A company has determined that its weekly total cost and total revenue (in dollars) for a...
A company has determined that its weekly total cost and total revenue (in dollars) for a product can be modeled by C(x) = 4000 + 30x R(x) = 300x -0.001x^2, where x is the number of items produced and sold. If the company can produce a maximum of 100,000 items per week, what production level will maximize profit?
A manufacturer estimates that its product can be produced at a total cost of C(x) =...
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.
Cost, revenue, and profit are in dollars and x is the number of units. Suppose that...
Cost, revenue, and profit are in dollars and x is the number of units. Suppose that the total revenue function for a product is R(x) = 55x and that the total cost function is C(x) = 2200 + 35x + 0.01x2. (a) Find the profit from the production and sale of 500 units. (b) Find the marginal profit function (c) Find MP at x = 500. Explain what it predicts. The total profit will ------ by approximately $------- on the...
The total cost and the total revenue​ (in dollars) for the production and sale of x...
The total cost and the total revenue​ (in dollars) for the production and sale of x ski jackets are given by   ​C(x)=26x+20,440   and   R(x)=200x-.2x^2 for 0 ​(A) Find the value of x where the graph of​ R(x) has a horizontal tangent line. ​(B) Find the profit function​ P(x). ​(C) Find the value of x where the graph of​ P(x) has a horizontal tangent line. ​(D) Graph​ C(x), R(x), and​ P(x) on the same coordinate system for 0less than or equals≤xless...
assume that revenue, R(x), and cost, C(x), of producing x units are in dollars: R(x)=9x-2x^2 C(x)=x^3...
assume that revenue, R(x), and cost, C(x), of producing x units are in dollars: R(x)=9x-2x^2 C(x)=x^3 - 3x^2 +4x +1 how many units must be produced to maximize profit? what is the maximum profit as a dollar amount?
If the cost function (in thousands of dollars) for a product is C(x) = 56x+182 (where...
If the cost function (in thousands of dollars) for a product is C(x) = 56x+182 (where x represents thousands of the product), and the price function in p = 256-50x, what price and quantity will maximize profit? What will this profit be? (Hint Profit = Revenue - Cost)
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT