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
balandron [24]
3 years ago
10

The unit cost, in dollars, to produce tubs of ice cream is $18 and the fixed cost is $11610. The price-demand function, in dolla

rs per tub, is p(x)=374-2x.
Find the cost C(x).
Find the revenue function R(x).
Find the profit function P(x).
At what quantity is the smallest break-even point?
Mathematics
1 answer:
Trava [24]3 years ago
4 0

Answer:

Step-by-step explanation:

Let x represent the number of tubs of ice cream that was produced.

The unit cost, in dollars, to produce tubs of ice cream is $18 and the fixed cost is $11610. This means that the total cost of producing x tubs of ice cream would be

C(x) = 18x + 11610

The price-demand function, in dollars per tub, is p(x)=374-2x.

The revenue function is product of the output by the price function

R(x) = x × p(x) = xp(x)

R(x) = x(374 - 2x) = 374x - 2x²

The profit function P(x) = R(x) - C(x)

Therefore,

P(x) = 374x - 2x² - (18x + 11610)

P(x) = 374x - 2x² - 18x - 11610

P(x) = - 2x² + 374x - 18x - 11610

P(x) = - 2x² + 356x - 11610

At the break even point,

Revenue = total cost.

Therefore,

374x - 2x² = 18x + 11610

2x² + 18x - 374x + 11610 = 0

2x² - 356x + 11610 = 0

Dividing through by 2, it becomes

x² - 178x + 5805 = 0

Applying the general formula for quadratic equations,

x = [- b ±√(b² - 4ac)]/2a

x = [- - 178 ±√(-178² - 4 × 1 × 5805)]/2 × 1

x = [178 ±√(31684 - 23220)]/2

x = [178 ±92]/2

x = (178 + 92)/2 or (178 - 92)/2

x = 135 or x = 43

Therefore, the quantity for the smallest break-even point is 43.

You might be interested in
I need help! If you can help me with this I can mark you!
Alina [70]

Answer:

I think it is 82 degrees or 102 degrees depend if you pick the 10s or 100s

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Common ratio of 135,45, 15, 5,
olchik [2.2K]

9514 1404 393

Answer:

  1/3

Step-by-step explanation:

If the ratio is common, you can choose any successive numbers to compute it. Smaller numbers may be more familiar. The ratio is ...

  5/15 = 1/3

4 0
3 years ago
Find the next term is in the explicit and recursive rule for the in term of the sequence. NO LINKS!!!
BARSIC [14]

9514 1404 393

Answer:

  5) 729, an=3^n, a[1]=3; a[n]=3·a[n-1]

  6) 1792, an=7(4^(n-1)), a[1]=7; a[n]=4·a[n-1]

Step-by-step explanation:

The next term of a geometric sequence is the last term multiplied by the common ratio. (This is the basis of the recursive formula.)

The Explicit Rule is ...

  a_n=a_1\cdot r^{n-1}

for first term a₁ and common ratio r.

The Recursive Rule is ...

  a[1] = a₁

  a[n] = r·a[n-1]

__

5. First term is a₁ = 3; common ratio is r = 9/3 = 3.

Next term: 243×3 = 729

Explicit rule: an = 3·3^(n-1) = 3^n

Recursive rule: a[1] = 3; a[n] = 3·a[n-1]

__

6. First term is a₁ = 7; common ratio is r = 28/7 = 4.

Next term: 448×4 = 1792

Explicit rule: an = 7·4^(n-1)

Recursive rule: a[1] = 7; a[n] = 4·a[n-1]

7 0
3 years ago
Please help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
NISA [10]
Last one I think so
6 0
3 years ago
Read 2 more answers
write an equation for a function at has a graph with the given characteristics. the shape of y=|x| is reflected across the y-axi
Luba_88 [7]
Refrection across the y-axis changes the function to y = |-x|.
Vertical stretch by a factor of 1.5 changes the graph to y = 1.5|-x|
Shifting the graph by 4 units downward changes the graph to y = 1.5|-x| - 4

Required equation is y = 1.5|-x| - 4
6 0
3 years ago
Other questions:
  • A number that tells how many times the base is used as a factor
    13·1 answer
  • 300/ 8 Please don't tell me a decimal!!!
    5·2 answers
  • Need some math help!!! <br> Factor the polynomial by grouping: 12p^3 − 21 p^2 + 28p − 49
    5·2 answers
  • What is 226 rounded to the nearest hundred
    10·2 answers
  • What is the linear equation for slope= 5 (4,7)
    5·1 answer
  • True or false question someone plz help I’ll cash app !
    13·2 answers
  • Look at each situation. Is it represented by the equation -3 + 3 = 0? Highlight the scenarios that match the equation
    9·1 answer
  • FILL IN THE BLANKS: Given P(x) = 3x5 + 7x6 + 11x7 – 12x - 10
    12·1 answer
  • The function f(x) = x2 is transformed to obtain the graph of the related function g(x) using a vertical stretch by a factor of 3
    8·1 answer
  • Question 3 of 32
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!