Question

The marketing department of a business has determined that the demand for a product can be...

The marketing department of a business has determined that the demand for a product can be modeled by p = 24 √ x , where p is the price per unit (in dollars) and x is the number of units. The cost (in dollars) of producing x units is given by C = 0.5x + 500. What price will yield a maximum profit?

Math   Calculus   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

Demand function

Revenue

cost function

Profit = Revenue - Cost

Differentiating with respect to x

For critical points

units

so x=576 is maxima point

dollars

Price

dollars per unit

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
A commodity has a demand function modeled by p = 103 − 0.5x and a total...
A commodity has a demand function modeled by p = 103 − 0.5x and a total cost function modeled by C = 30x + 31.75, where x is the number of units. (a) What price yields a maximum profit? (b) When the profit is maximized, what is the average cost per unit? (Round your answer to two decimal places.)
1. A. The Cobb-Douglas production function, f(x,y)=40x^1/4y^3/4, describes the production of a company for which each...
1. A. The Cobb-Douglas production function, f(x,y)=40x^1/4y^3/4, describes the production of a company for which each unit of labor costs $100 and each unit of capital costs $125. For a new project, the company has allocated $60,000 for labor and capital. Find the amount of money that the company should allocate to labor and capital to maximize production. B. The marketing department of a business has determined that the demand for a product can be modeled by p=(50/(square root of...
2) Product price (p) and demand (D) are typically related linearly. Company A has performed extensive...
2) Product price (p) and demand (D) are typically related linearly. Company A has performed extensive market research to develop a better relationship. They determined that the selling price of a product, p, is related to the demand for their product, D, in accordance with the following improved relationship P= 92.5 – 0.09 (D^1.1) (in dollars) Demand is given in units per year. In addition, there is a fixed cost of $40,000 per year and a variable cost of $40...
Your marketing department has determined that the price you can expect to sell the appliances for...
Your marketing department has determined that the price you can expect to sell the appliances for is approximated by the demand curve p =400e^( –0.0006D) + 75. Your setup cost to produce up to 10000 appliances per month is $50,000 and the incremental cost per appliance is $50. Plot profit as a function of demand and determine the optimal value of demand.
5) The cost per unit of producing a product is 60 + 0.2x dollars, where x...
5) The cost per unit of producing a product is 60 + 0.2x dollars, where x represents the number of units produced per week. The equilibrium price determined by a competitive market is $220. How many units should the firm produce and sell each week to maximize its profit? b) What is the maximum profit?
The weekly demand function for x units of a product sold by only one firm is...
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...
The marketing research department of a computer company used a large city to test market the...
The marketing research department of a computer company used a large city to test market the firm’s new laptop. The department found that the relationship between price p (dollars per unit) and the demand x (units per week) was given approximately by p=1,296-0.12x^2 0≤x≤80) So, weekly revenue can be approximated by R(x)=xp=1,296x-0.12x^3 Find all critical numbers of the function, then use the second-derivative test on each critical number to determine if it is a local maximum or minimum in order...
The price of a product in a competitive market is $500. If the cost per unit...
The price of a product in a competitive market is $500. If the cost per unit of producing the product is 140 + 0.1x dollars, where x is the number of units produced per month, how many units should the firm produce and sell to maximize its profit? units
The weekly demand function for x units of a product sold by only one firm is...
The weekly demand function for x units of a product sold by only one firm is p = 300 − 1 2 x dollars, and the average cost of production and sale is C = 200 + 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?
1. Suppose you’re given the following: a) the demand equation p for a product, which is...
1. Suppose you’re given the following: a) the demand equation p for a product, which is the price in dollars, and x is the quantity demanded b) C(x), which is the cost function to produce that product c) x ranges from 0 to n units Q. Describe briefly how you would maximize the profit function P(x), the level of production that will yield a maximum profit for this manufacturer.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT