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
AVprozaik [17]
3 years ago
12

Acrosonic's production department estimates that the total cost (in dollars) incurred in manufacturing x ElectroStat speaker sys

tems 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.
C(x) = 270x + 18000 and R(x) = -0.04x2 + 800x

a) Find the profit function P.

b) Find the marginal profit function P'.

c) Computer the following values.
P'(4000)
P'(9500)
Mathematics
1 answer:
il63 [147K]3 years ago
6 0

Answer:

a)  P(x)=-0.042x^2+530x-18000

b)  P'(x)=-0.084x+530

c)

P'(4000)=194

P'(9500)=-268

Step-by-step explanation:

a)

We know that Revenue is our total income and cost is our total cost. Thus, profit is what's left after cost is subtracted from Income (revenue). Thus, we can say:

P(x) = R(x) - C(x)

Finding Profit Function (P(x)):

P(x) = R(x) - C(x)\\P(x) = -0.042x^2+800x-(270x+18000)\\P(x)=-0.042x^2+800x-270x-18000\\P(x)=-0.042x^2+530x-18000

This is the profit function.

b)

The marginal profit is the profit earned when ONE ADDITIONAL UNIT of the product is sold. This is basically the rate of change of profit per unit. We find this by finding the DERIVATIVE of the Profit Function.

Remember the power rule for differentiation shown below:

\frac{d}{dx}(x^n)=nx^{n-1}

Now, we differentiate the profit function to get the marginal profit function (P'):

P(x)=-0.042x^2+530x-18000\\P'(x)=2(-0.042)x^1+530x^0-0\\P'(x)=-0.084x+530

This is the marginal profit function , P'.

c)

We need to find P'(4000) and P'(9500). So we basically put "4000" and "9500" in the marginal profit function's "x". The value is shown below:

P'(x)=-0.084x+530\\P'(4000)=-0.084(4000)+530\\P'(4000)=194

and

P'(x)=-0.084x+530\\P'(9500)=-0.084(9500)+530\\P'(9500)=-268

You might be interested in
Express 0.52 as a fraction
ioda
52/100
26/50
13/25
These will all do.
7 0
3 years ago
Read 2 more answers
Tom always keeps his 4 gardens clean. He takes 20 minutes to clean a single garden. How much time will it take to clean all four
Nataly [62]


If each garden takes 20 minutes to clean, it will take him (20 x 4) to clean the gardens.

20 x 4 = 100

80 minutes

or 1 hour and 10 minutes.

5 0
3 years ago
Read 2 more answers
Solve the system of inequalities to decide if the point (-3,2) is part of the solution; y<=-4x-3, +8y>=7
inna [77]

Answer:

(x,y) = (-3,2) is a solution

Step-by-step explanation:

Given

y \le -4x + 3

x + 8y \ge 7

Required

Determine if (x,y) = (-3,2) is a solution

y \le -4x + 3 becomes

2 \le -4 * -3 + 3

2 \le 15 --- this is true

x + 8y \ge 7

-3+ 8 * 2 \ge 7

13 \ge 7 --- this is also true

Hence,

(x,y) = (-3,2) is a solution

6 0
2 years ago
Can somebody please hellllp me with thissssss!!! please
erastova [34]

Answer:

A

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
PLEASE ANSWER THIS IS REALLY IMPORTANT!!!
Elan Coil [88]
Answer: C
Explanation: The y-intercept which is -9 matches with the equation and the slope matches too
4 0
2 years ago
Read 2 more answers
Other questions:
  • A used motorcycle is priced at $3,438. If you borrow the money for the motorcycle, your payments will be $165 a month for 24 mon
    10·1 answer
  • What does -2 raised by 10 equal to?
    14·2 answers
  • Zack needs $299.99 to buy the new bike he wants. He has saved $150 so far toward the new bike. From this week on, he will save $
    11·2 answers
  • Estimate the weight of a piece of cake.
    12·2 answers
  • Sam makes candles. She has two pounds of candle wax which she poured into eight molds. What is the average of each mold?
    10·1 answer
  • What is the answer. If you go into a detailed description I will mark you as branliest.
    13·1 answer
  • Marisol sells wedding cakes. She charges a flat fee of $245 to make the wedding cake, plus an additional $120 per tier of cake.
    13·1 answer
  • If you answer correctly I will give you brainliest.
    14·1 answer
  • Solve −x−6≥−5 or −2x−5>4 and write the solution in interval notation. Note: Use improper fractions, if necessary.
    15·1 answer
  • Solve for p.
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!