We appreciate your visit to The marginal profit for the new X 99 pogo stick is P x 0 2x 100 where x is the number of sticks produced and. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
The profit function for the new X−99 pogo stick is P(x) = [tex]-0.1x^2 + 100x - 750[/tex]. The level of production of pogo sticks (x) that produces a maximum profit is 500. The dollar value of the maximum profit is 25,000.
The profit of a company is given by the product of the price of its products and the number of units sold. A profit function can be expressed using the given marginal profit equation P′(x) = −0.2x + 100 as follows.
P(x) = ∫ P′(x) dx + C = [tex]-0.1x^2 + 100x + C[/tex] Where C is the constant of integration, and since the profit is given to be - $1000 when 50 sticks are produced and sold, the value of C can be found as shown below.
[tex]-1000 = -0.1(50)^2 + 100(50) + C[/tex]
C = -750
Hence, the profit function is given by P(x) =[tex]-0.1x^2 + 100x - 750[/tex]
a) Find the profit function.The marginal profit equation is given as P′(x) = −0.2x + 100
By integrating the marginal profit function, we can obtain the profit function:
∫ P′(x) dx =[tex]-0.1x^2 + 100x + C[/tex]
Profit function is given by P(x) = [tex]-0.1x^2 + 100x - 750[/tex]
b) We can find the level of production of pogo sticks (x) that produces a maximum profit by using the formula:
x = -b/2a where a = -0.1 and b = 100x = -100/2(-0.1) = 500
Therefore, the level of production of pogo sticks (x) that produces a maximum profit is 500.
c) To find the dollar value of the maximum profit, substitute the value of x obtained in part (b) into the profit function: [tex]P(500) = -0.1(500)^2 + 100(500) - 750[/tex]
P(500) = $25,000
Therefore, the dollar value of the maximum profit is $25,000.
Therefore, the profit function for the new X−99 pogo stick is [tex]P(x) = -0.1x^2 + 100x - 750[/tex]. The level of production of pogo sticks (x) that produces a maximum profit is 500. The dollar value of the maximum profit is $25,000.
To know more about constant of integration visit:
brainly.com/question/29166386
#SPJ11
Thanks for taking the time to read The marginal profit for the new X 99 pogo stick is P x 0 2x 100 where x is the number of sticks produced and. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
