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
Help please I don’t get this
Bess [88]

Answer:

y = -2x - 1

Step-by-step explanation:

Formula is y = mx + b

m = slope

slope = change in y/change in x = (-1 - 3) / (0 - -2) = -4/2 = -2

So equation is now y = -2x + b

To find b, substitute any value from the table into the equation. Let's use (-2,3)

y = -2x + b

3 = -2(-2) + b

3 = 4 + b

-1 = b

So equation is y = -2x - 1

3 0
3 years ago
Read 2 more answers
Order the following numbers from least to greatest:
erik [133]
See the photo attached. The boxed answer is the corrected answer

5 0
3 years ago
Help me out asap!please and thank you
irga5000 [103]

Answer:

c. (5, -2)

Step-by-step explanation:

as we can clearly see, the 4th vertex has to be on the positive side of x.

therefore, all answer options with negative x are out.

(2, -5) is almost at D (-1, 5). that cannot be right for a rectangle.

that leaves only c as right answer.

FYI - how to get this without predefined answer portions ?

the x- difference of B to A is 4 (from -5 to -1). the x-difference from D to C must be the same (4). 1 + 4 = 5.

so, x of D must be 5.

the y- difference of B to A is 3 (from 3 to 6). the y-difference from D to C must be the same (3). -5 + 3 = -2.

so, y of D must be -2.

3 0
1 year ago
How do you find square roots? Example: Square root of 441.
Alecsey [184]
There isn't really a formula for higher numbers. you can use a calculator with the square root function
6 0
3 years ago
The midsegment of a trapezoid is always parallel to each base true or false
Deffense [45]

Answer:

True

Step-by-step explanation:

we know that

The <u><em>Trapezoid Mid-segment Theorem</em></u> states that : A line connecting the midpoints of the two legs of a trapezoid is parallel to the bases, and its length is equal to half the sum of lengths of the bases

see the attached figure to better understand the problem

EF is the mid-segment of trapezoid

EF is parallel to AB and is parallel to CD

EF=(AB+CD)/2

so

The mid-segment of a trapezoid is always parallel to each base

therefore

The statement is true

8 0
3 years ago
Other questions:
  • Write 27 : 28 as a ration in its simplest form
    14·2 answers
  • Which ordered pair makes the equation true 2x - 5y = -10
    15·1 answer
  • Write 9,540,000 in expanded form using exponents to show powers of 10
    5·1 answer
  • Make r the subject of the formula:<br><br> A= πr²
    10·2 answers
  • (5y - 1) + (-2y + 4)
    13·2 answers
  • the radius of a circle with an area of a circle with an area of 60 square centimeters is represented by the expression sqrt 60/x
    12·1 answer
  • in right triangle ABC, angle C is a right angle, AB is 25 units long, and BC is 24 units long. What is the lenght of AC?
    15·1 answer
  • Estimate the square root to the nearest hundreths.
    8·1 answer
  • Help !! 10 points!! :)
    15·1 answer
  • What is the shortest strip of fiber from which five pieces of the following lengths can be cut: 9 1/2 inches, 10 11/16 inches, 6
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!