1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
lisabon 2012 [21]
3 years ago
9

If C ( x ) = 11000 + 500 x − 3.6 x 2 + 0.004 x 3 is the cost function and p ( x ) = 1700 − 9 x is the demand function, find the

production level that will maximize profit. (Hint: If the profit is maximized, then the marginal revenue equals the marginal cost.)
Mathematics
1 answer:
Bess [88]3 years ago
5 0

Answer:

Step-by-step explanation:

The cost function = C(x)

The demand function = P(x)

C(x) = 11000 + 500x - 3.6x^2 + + 0.004x^3

P(x) = 1700 - 9x

Differentiate C(x) with respect to x

C'(x) = 500 - 7.2x + 0.012x^2

C'(x) is the marginal cost

Revenue = x. P(x)

R(x) = x( 1700 -9x)

= 1700x - 9x^2

Differentiate R(x) with respect to x

R'(x) = 1700 - 18x

R'(x) is the marginal revenue

Profit is maximized when R'(x) = C'(x)

1700 - 18x = 500 - 7.2x + 0.012x^2

Collect like terms

0 = 500 - 1700 - 7.2x +18x +0.012x^2

0 = -1200 + 10.8x +0.012x^2

0 = 0.012x^2 + 10.8x - 1200

Using x=( -b +_ √b^2 - 4ac) /2a

a = 0.012 , b= 10.8 , c= -1200

x= (-10.8 +_ √(10.8^2) - 4*0.012*(-1200)) /2*0.012

= ( -10.8 +_√116.64 + 57.6) / 0.024

= (-10.8 +_ √174.24) / 0.024

= (-10.8 +_13.2) / 0.024

= (-10.8+13.2)/0.024 or (-10.8 - 13.2)/0.024

= 2.4/0.024 or -24/0.024

x= 100 or -1000

Since our profit cannot be negative, the profit = $100

You might be interested in
Solve for h: v = pi squared multiplied by h h = V multiplied by pi over r squared h = V over pi r squared h = V plus pi r square
alexandr1967 [171]

Hello from MrBillDoesMath

Answer:

See below for steps.

Discussion:

As I understand the problem statement we have a cylinder of height h and radius r. The volume of the cylinder is given by the formaul:

V = (pi * r^2) h

Divide both sides by (pi * r^2):

V\ (pi * r^2)) =     ( (pi * r^2) * h ) \ ((pi * r^2)   =>

V\ (pi * r^2)  = 1 * h = h  as  (pi * r^2)   \ (pi * r^2))

Therefore, h =  V\ (pi * r^2)



Thank you,

Mr. B


7 0
3 years ago
Read 2 more answers
So I need help pls show ur work
Ad libitum [116K]

Answer:

x = – ⅓

Step-by-step explanation:

The solution to the expression can be obtained as follow:

–3.1x + 7 – 7.4x = 1.5x – 6(x – 3/2)

Clear bracket

–3.1x + 7 – 7.4x = 1.5x – 6x + 9

–3.1x – 7.4x + 7 = –4.5x + 9

–10.5x + 7 = –4.5x + 9

Collect like terms

–10.5x + 4.5x = 9 – 7

–6x = 2

Divide both side by –6

x = 2 / –6

x = – ⅓

Thus, the solution to the equation is –⅓

7 0
3 years ago
Solve the Quadratic Equation By Completing the Square<br> b^2-15b-54=0
vladimir1956 [14]
b^{2}-15b-54=0. \newline&#10;b^{2}-15b=54. \newline&#10;b^{2}-15b+(\frac{15}{2})^{2}=54+(\frac{15}{2})^{2}. \newline&#10;(b-\frac{15}{2})^{2}=\frac{441}{4}. \newline&#10;b-\frac{15}{2}=\pm\frac{21}{2}. \newline&#10;b=\pm\frac{21}{2}+\frac{15}{2}. \newline&#10;b_1 = -3, b_2 = 18.
3 0
3 years ago
factor 3a^5-18a^3+6a^2, I know the answer is 3a^2(a^3-6a+2) but I am so lost on how to get the factor of 3a^2..How in the world
rusak2 [61]

Answer:

\huge\boxed{3a^2(a^3-6a+2)}

Step-by-step explanation:

\sf 3a^5-18a^3+6a^2\\\\HCF = 3a^2\\\\Take \ 3a^2 \ common\\\\= 3a^2(a^3-6a+2)\\\\\rule[225]{225}{2}

Hope this helped!

<h3>~AH1807</h3>
5 0
2 years ago
Please help
Anettt [7]

Answer:

24

Step-by-step explanation:

7 0
3 years ago
Other questions:
  • I am thinking of a number. It is increased by 7. The sun is 21. What is my number?
    11·2 answers
  • Jim has calculated the area of a rectangle to be x^3+x^2+x+1. If the width of the rectangle is x+1, then it's length is
    15·2 answers
  • HELLLLLLP
    5·1 answer
  • What number multiplied by itself 3 times equals 10
    6·1 answer
  • What is the surface area of the right rectangular prism ?​
    6·1 answer
  • Tram left a tip of $9, which was StartFraction 3 over 20 EndFraction of the total cost of the food. Which shows the correct equa
    13·1 answer
  • A box contains 4 red cubes, 3 blue cubes, 2 green cubes, and 1 yellow cube. You pick two cubes at random, replacing each after y
    9·2 answers
  • 12 (X + 2) - 4x = 4( 2X + 11 ) -20<br><br>Solve for X ​
    9·1 answer
  • Choose the equation of the the ellipse shown in the graph.
    9·1 answer
  • The geometric sequence an = 1/5an-1 with an initial value of a1 = 125 represents the sales of a specific
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!