The daily cost, in dollars, to produce x Sasquatch Berry Pies is C(x) = 3x + 36, x ≥ 0 and
the price-demand function, in dollars per pie, is p(x) = 12 − 0.5x, 0 ≤ x ≤ 24. Find the price to charge per item in order to maximize profit.

Answers

Answer 1

The cost per item for maximum profit is $7.50 .

The maximum and minimum value of a function f(x) is calculated by finding the first and second derivative of f(x).

If f"(x)<0 then the function f(x) has a maximum value for x at f'(x)=0.If f"(x)>0 then the function f(x) has a minimum value for x at f'(x)=0.

The cost to produce x pies is given by the cost function

[tex]C(x)=3x+36[/tex]

The price demand function for each pie is given by

[tex]p(x)=12-0.5x[/tex]

Revenue gained from selling x pies

[tex]R(x)=x\times p(x)\\or,R(x)=x\times(12-0.5x)\\or,R(x)=12x-0.5x^2[/tex]

Now profit function is given by

[tex]P(x)=R(x)-C(x)\\or,P(x)=-0.5x^2+12x-3x-36\\or,P(x)=-0.5x^2+9x-36[/tex]

Now we have to find the maximum profit. We know that for a function

[tex]P(x)=-0.5x^2+9x-36\\P'(x)=-x+9[/tex]

[tex]P''(x)=-1[/tex]

At P'(x)=0

or,-x+9=0

or, x=9

As P''(x)<0 therefore the profit function P(x) is maximum for x at P'(x)=0.

The profit is maximum at x=9

Price to charge per item=12-0.5x

Substituting the value of x we get:

[tex]p(x)=12-(0.5\times 9)\\or,p(x)=12-4.5\\or,p(x)=7.5[/tex]

Therefore the cost per item for maximum profit is $7.50 .

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Related Questions

The mean diameter of holes produced by a drilling machine is 4.05mm and the standard deviation of the diameter is 0.0028mm. for 20 holes drilled using this machine. determine , correct to the nearest whole number how many hare likely to have diameters of between
a) 4.048 and 4.0553
assuming they are normaly distributed

Answers

The hole having the diameters likely between 4.048 and 4.0553 is 17.

Maximum value of diameter = 4.05 + 0.0028 = 4.0528

Minimum value of diameter = 4.05 - 0.0028 = 4.0472

So, the diameters of the holes are in AP with common difference

= (2 × 0.0028) / 20 = 0.00028

So, the AP is:

4.0472, 4.04748, 4.04776, 4.04804, …, 0.0.0528

So, the first 3 terms are not included between 4.048 and 4.0553

Hence, the answer is 20 - 3 = 17

Therefore, the hole having the diameters likely between 4.048 and 4.0553 is 17.

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find the distance between the two points in simplest radical form. (-2,1) and (-8,-7)

Answers

Answer:

10

Step-by-step explanation:

Use the distance formula to determine the distance between two points.
√[(x₂ - x₁)² + (y₂ - y₁)²]

HELP PLEASE!!!!!! Anaya bought a sweater that was on sale. The sweater originally cost $34.50 but was purchased for $27.60. What percentage of the original price was the discount?

Answers

Answer: 80%. Hope this helps, please consider making me Brainliest.

Step-by-step explanation:

To find the percentage, divide the sale cost by the original cost:

27.60/34.50

Let's multiply both sides by 10 to make the operation easier:

27.6/34.5 ( I eliminated the zero's because they kind of have no use) -->

276/345, now solve:

276/345 = 0.8

0.8 = 80%

The percentage is 80%.

Solve for f can somebody help

Answers

Answer: f < 9

Step-by-step explanation:

first, cross multiply 2 and 2:

f - 5 < 4

f < 9

Answer:

f < 9

Step-by-step explanation:

=> (f-5)/2 < 2

multiplying both sides by 2

=> 2(f-5)/2 < 2×2

=> f-5 < 4

adding 5 to both sides

=> f-5+5 < 4+5

=> f < 9

A quadratic function has A) straight lines that do both increase, decrease or stay constant on the same graph. B) curved lines that only increase or decrease. C) curved lines that do both increase and decrease on the same graph. D) straight lines that only increase or decrease. E) straight lines that do both increase and decrease on the same graph

Answers

Slay you got to do some things with your hands on you lol I

On a map the distance between two towns is 2.6 cm to scale of the map is 1 cm 50 km what is the actual distance between two

Answers

The answer to this question is:

The actual distance between the two towns = 130 km

Given that according to  the map scale,

Distance between two towns = 2.6cm

Given that the scale of map =

                                           1cm = 50km

So, we are asked to find the actual distance between them.

For finding the distance between two towns, we have to multiply the distance from the map by the scale of the map.

Distance between two towns * scale of the map

= 2.6 * 50 km

= 130 km

Therefore, actual distance between the two towns = 130 km

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How many solutions does the following system of equations have? 5x−2y=10 y=5/2x-5

Answers

Answer:

Infinite number of solutions

No unique solution

Step-by-step explanation:

5x - 2y = 10    (1)

y = 5/2x - 5       (2)

Multiply (2) by 2 to get
2y = 5x - 10  

Rewrite the above equation as 5x - 2y = 10 (3)

Since both equations are the same, we are provided with a single equation in 2 variables there are infinite solutions

Simplify the expression.
(4 × 6)y=

Answers

Answer:

24y^2

Step-by-step explanation:

4y x 6y =

24y ^2

24y to the second power

HELP ME AGINS SNDJJEJEJE

Answers

Answer: 0

Step-by-step explanation:

-2+-1 = -3

-3+0 = -3

-3+1 = -2

-2+2 = 0

|1/4 x +2| -3 =5 solve for x and graph on number line

Answers

The value of x on the number line is 24 and - 40

A number line in elementary mathematics is a representation of a graduated straight line that acts as an abstraction for real numbers, represented by the letter R. It is assumed that every point on a number line corresponds to a real number, and that every real number corresponds to a point.

When seen as a geometric space, namely the one-dimensional Euclidean space, the number line, also known as a real line in advanced mathematics, is technically defined as the set R of all real numbers. It can be conceptualized as a linear continuum, metric space, topological space, vector space (or affine space), measure space, or topological space.

The given equation is

[tex]|\frac{1}{4}x+2 | -3=5[/tex]

Solving the equation:

[tex]or,|\frac{1}{4}x+2 | =5+3\\or,|\frac{1}{4}x+2 |=8\\or,\frac{1}{4}x+2=\pm8\\or,x+8=\pm32\\or,x=-8\pm32[/tex]

Now we take the two separate values of x:

either x=-8+32 or x=-8-32

or,x=24 or x=-40

The value of x is 24 and - 40.

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Find the sum of 3√2 and 2√8 in simplest form. Also, determine whether the result
is rational or irrational and explain your answer.

Answers

Answer:

7√2

7√2 is irrational since √2 is irrational

Step-by-step explanation:

3√2 + 2√8 = 3√2 + 2 × 2√2 = 3√2 + 4√2 = 7√2

7√2 is irrational since √2 is irrational

604,542+87,106 estimated

Answers

Answer:

the answer is to the question is 691648

mr drew wants to build a square sandbox with an area of 100 square feet. What is the length of wood Mr.Drew needs to.make the sides of the sandbox

Answers

Answer is 10’ boards to make a square
10’ x 10’ x 10’ x 10’ sandbox.

Reason

Area of a square is Side^2.

We know the area of the square is 100

So take √100 = 10

Problem solved!

a boy weighs 90 pounds on earth but 34.5 pounds on mars how much does a 600 pound man weigh on mars

Answers

Answer:

230lb

Step-by-step explanation:

The Boy weighs 90 lb on earth and 34.5 on the Moon.

90/34.5= 2.608695652

The boys weight on earth divided by his weight on the moon is equal to the difference in weight

So for a 600 lb guy

600/2.608695652 = 230

The guys Earth weight divided by the difference in weight is equal to his moon weight.

4x^2-7; x= -2

4x^2-7x =

Answers

Step-by-step explanation:

f(x) = 4x² - 7 , x = -2

= 4x² - 7

= 4.(-2)² - 7

= 4.4 - 7

= 16 - 7

= 9

Please help also I know the answers there are wrong
If possible explain how you got the answers

Answers

The values of all the required angles are; m∠5 = 42°; m∠8 = 138°; m∠10 = 138° and m∠11 = 42°

How to Identify corresponding angles?

Corresponding angles are formed where a line known as an intersecting transversal, crosses through a pair of straight lines.

Now, we are given that; m∠1 = 42°

By corresponding angles, we can say that;

m∠1 = m∠5

Thus; m∠5 = 42°

Now, we know that sum of angles on a straight line is equal to 180° i.e. they are supplementary angles.

Now, from the diagram, we can see that m∠5 and m∠8 are supplementary angles and as such;

m∠5 + m∠8 = 180°

42 + m∠8 = 180

m∠8 = 180° - 42°

m∠8 = 138°

Now, m∠9 is a corresponding angle to both m∠1 and m∠5. Thus, we can say that; m∠9 = 42°. However, m∠9 is supplementary to m∠10. Thus;

m∠10 = 180 - 42

m∠10 = 138°

Lastly, m∠10 and m∠11 are supplementary angles and as such;

m∠10 + m∠11 = 180°

138 + m∠11 = 180

m∠11 = 180° - 38°

m∠11 = 42°

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Which equation represents the graph of this function?
_
A ) f(x)= √ x −4
____
B) f(x)= √x + 4
____
C) f(x)= √x - 4
_
D) f(x)= √x + 4

Answers

Answer:

USE air math

Step-by-step explanation:

hope that helps

please help with this question the question is in the attached image

Answers

The coefficient matrix for the given system of equations is as follows:

[tex]\left[\begin{array}{ccc}2&-6&-1\\-10&9&5\\3&0&5\end{array}\right][/tex]

What is a system of equations?

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

The augmented matrix of a system is composed as follows:

The first column has the coefficients of x.The second column has the coefficients of y.The last column has the results, that is, the values of the other side of the equality.

In standard notation, this system is given as follows:

2x - 6y = -1.-10x + 9y = 5.3x + 0y = 5.

Hence the augmented matrix is given by:

[tex]\left[\begin{array}{ccc}2&-6&-1\\-10&9&5\\3&0&5\end{array}\right][/tex]

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*Please help*
Xavier bought a new boat for $24,000 in the year 2009. He knows that the value of the boat has depreciated linearly. If the value of the boat in 2010 was $18,500, what was the annual rate of change of the boat's value? Round your answer to the nearest hundredth if necessary.

Answers

Answer:

5500 is correct Answer.

Please mark me as brainlist answer.

(13) Determine if the following equation has one solution, no solution, or infinite
solutions: 15y + 14 = 7(2y + 2).

Answers

Answer:

y = 0, one solution

Step-by-step explanation:

15y + 14 = 14 y + 14

-14y          -14y

y + 14 = 14

-14        -14

y = 0

so one solution

The answer to the question would be
zero, one solution.

Please solve this! I need it asap!

Answers

The differentiation of the given function is expressed as; 2x - √3(y) = 0

How to carry out Differentiation?

We want to differentiate the function;

x² - √3(xy) + 2y² = 12

To differentiate this means to express as;

x²(dy/dx)  - √3(xy)(dy/dx) + 2y²(dy/dx) = 12(dy/dx)

This gives us;

2x - √3(y) + 0 = 0

2x - √3(y) = 0

Thus, the differentiation of the given function is expressed as;

2x - √3(y) = 0

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I Use the quadratic equation to complete the following sentence
2 - 4x + 10 = 0
The quadratic equation has
Select One

Answers

Answer:

your answer is 7/2

What is an equation of the line that passes through the point ( − 3 , − 1 ) (−3,−1) and is perpendicular to the line x − 2 y = 6 x−2y=6?

Answers

The equation of the line passing through given points (-3, -10) and perpendicular to other is y + 2x + 7 = 0.

When the equation of line in point-slope form?A line's equation in point slope form is (y - y₁) = m. (x – x₁). As a result, the equation of a line with slope m passing through the origin is: y - 0 = m(x = 0), i.e. y = mx.where m is the line's slope and  (x₁,  y₁) are the coordinates of a provided point on the line .

The equation of the perpendicular line is given as;

x − 2y = 6

Write the equation in standard form;

y = x/2 - 3

Where, slope of the line m₁ is (1/2) and y -intercept is (-3).

The other line passing perpendicular on this line has a slope: m₂.

The relation between slopes of perpendicular lines are-

m₁ × m₂ = -1

m₂ = -1/m₁

m₂ = -1/(1/2)

m₂ = -2

Now, the coordinates of the line are: (-3, -1)

The equation of the line will be;

(y - y₁) = m₂ (x – x₁)

Put the values;

(y - (-1)) = -2(x - (-3))

y + 1 = -2x - 6

y + 2x + 7 = 0

Thus, the equation of line is y + 2x + 7 = 0.

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Write a subtraction expression using integers that equals -6

Answers

If it’s asking for an equation than -10-(-4)=-6 should work but I’m not sure

is 1/8 equivalent to 2/12

Answers

Answer:

No

Step-by-step explanation:

Check by changing to a common denominator

Answer: no

Explanation: start by finding a common denominator in this case it’ll be 24
1 x 3 3 | 2 x 2 4
- = - - | - = -
8 x 3 24. | 12 x 2 24

After this you can see there’s a one number difference

The difference between two numbers is 2811.
The bigger number is 4200.
What is the smaller number?

Answers

The smaller number is 1389. We get this by using the technique of subtracting the bigger from the smaller number and equate it to the difference product.

Given the difference between two numbers is 2811.

The bigger number is 4200.

The smaller number is = ?

let the smaller number be 'x'

as the statement says difference between two numbers = 2811

Subtract the largest number from the smallest number to determine the difference between two integers. This sum is a product, and the difference between the two values is the product.

⇒ bigger number ₋ smaller number = 2811

⇒ 4200 ₋ x = 2811

⇒ ₋ x = 2811 ₋ 4200

⇒ ₋ x = ₋ 1389

cancel the negative sign from both sides.

x = 1389

hence we get the smaller number as 1389.

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Would like help with this?

Answers

The largest interval in which the function is continuous is given by:

(-∞, -3).

What is the continuity concept?

A function f(x) is continuous at x = a if it is defined at x = a, and:

[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]

A function is also not continuous for the values of x which are outside the domain of the function, hence a fraction is not continuous at the zeroes of the denominator.

In this problem, the zeroes of the denominator of the function are:

x = -3, x = 4.

Hence the continuity intervals are:

(-∞, -3).(3,4).(4,∞).

The largest one is the first, as |-3| < |4|, meaning that it is a larger distance from infinity.

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Fill the table below using the function f(x) = -2x^2 +5x-3
x | f(x)
-1.4 |
-0.7 |
0 |
0.7 |
1.4 |

+ Explain?

Answers

The complete table of values is

x     |   f(x)

-1.4  |  -13.92

-0.7 |  -7.48

0    |  -3

0.7 |   -0.48

1.4 |  0.08

How to fill the table using the function?

The function is given as:

f(x) = -2x^2 +5x - 3

Next, we calculate the values of the functions at the given x values

So, we have:

f(-1.4) = -2(-1.4)^2 + 5(-1.4) - 3 = -13.92

f(-0.7) = -2(-0.7)^2 + 5(-0.7) - 3 = -7.48

f(0) = -2(0)^2 + 5(0) - 3 = -3

f(0.7) = -2(0.7)^2 + 5(0.7) - 3 = -0.48

f(1.4) = -2(1.4)^2 + 5(1.4) - 3 = 0.08

Hence, the complete table of values is

x     |   f(x)

-1.4  |  -13.92

-0.7 |  -7.48

0    |  -3

0.7 |   -0.48

1.4 |  0.08

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Divide 556 by 4 USING LONG DIVISION.

What are the numbers under the 556?
Answer as 1st row under 556
Next row under
Next row under
Next row under
Next row under
Next row under
What is the final answer?

Answers

Answer: 139

Step-by-step explanation:

first, 4 can go into 5 once so you would put one down --> 5-5= 1

bring down the one and then put down the 5 from the tens place

4 can go into 15 three times which would be 15-12 = 3

so at the top, you would have 13 so far

then with the 3 left bring down the 6 from the hundreds place from the 556

lastly, since 4 can go into 36 nine times you would put 9 down next to 13 on the top which would make it 139

(Sorry if it doesn't make that much sense)

determine the values of the missing entries. reduce all fractions to the lowest terms
9x-6y= 18

Answers

By evaluating the given linear relation, we conclude that the complete table is:

x:  2, 0, 1, 14/3

y: 0, -3, -3/2, 4

How to determine the values of the missing entries?

Here we have the linear relation:

9x - 6y = 18

And we want to complete the given table, to do so, we just need to evaluate the relation in the given values and with that we can find the missing ones.

For example, the first pair has y = 0.

Evaluating that we get:

9x - 6*0 = 18

9x = 18

x = 18/9 = 2

Then we have the pair (2, 0).

The second has x = 0, replacing that we get:

9*0 - 6*y = 18

y = 18/-6 = -3

So we have the pair (0, -3)

The third has x = 1, replacing that:

9*1 - 6y = 18

-6y = 18 - 9 = 9

y = 9/-6 = -3/2

So we have the pair (1, -3/2)

The last value on the table is y = 4, replacing that:

9x - 6*4 = 18

9x - 24 = 18

9x = 18 + 24 = 42

x = 42/9 = 14/3

Then the complete table is:

x:  2, 0, 1, 14/3

y: 0, -3, -3/2, 4

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