A company manufactures and sells x television sets per month. The monthly cost and​ price-demand equations are ​C(x)=74,000+80x and p(x)=300− x 30​, 0≤x≤9000. ​(A) Find the maximum revenue. ​(B) Find the maximum​ profit, the production level that will realize the maximum​ profit, and the price the company should charge for each television set. ​(C) If the government decides to tax the company ​$5 for each set it​ produces, how many sets should the company manufacture each month to maximize its​ profit? What is the maximum​ profit? What should the company charge for each​ set?

Answers

Answer 1

Answer:

a) $675000

b) $289000 profit,3300 set, $190 per set

c) 3225 set, $272687.5 profit, $192.5 per set

Step-by-step explanation:

a) Revenue R(x) = xp(x) = x(300 - x/30) = 300x - x²/30

The maximum revenue is at R'(x) =0

R'(x) = 300 - 2x/30 = 300 - x/15

But we need to compute R'(x) = 0:

300 - x/15 = 0

x/15 = 300

x = 4500

Also the second derivative of R(x) is given as:

R"(x) = -1/15 < 0 This means that the maximum revenue is at x = 4500. Hence:

R(4500) = 300 (4500) - (4500)²/30 = $675000  

B) Profit P(x) = R(x) - C(x) = 300x - x²/30 - (74000 + 80x) = -x²/30 + 300x - 80x - 74000

P(x) = -x²/30 + 220x - 74000

The maximum revenue is at P'(x) =0

P'(x) = - 2x/30 + 220= -x/15 + 220

But we need to compute P'(x) = 0:

-x/15 + 220 = 0

x/15 = 220

x = 3300

Also the second derivative of P(x) is given as:

P"(x) = -1/15 < 0 This means that the maximum profit is at x = 3300. Hence:

P(3300) =  -(3300)²/30 + 220(3300) - 74000 = $289000  

The price for each set is:

p(3300) = 300 -3300/30 = $190 per set

c) The new cost is:

C(x) = 74000 + 80x + 5x = 74000 + 85x

Profit P(x) = R(x) - C(x) = 300x - x²/30 - (74000 + 85x) = -x²/30 + 300x - 85x - 74000

P(x) = -x²/30 + 215x - 74000

The maximum revenue is at P'(x) =0

P'(x) = - 2x/30 + 215= -x/15 + 215

But we need to compute P'(x) = 0:

-x/15 + 215 = 0

x/15 = 215

x = 3225

Also the second derivative of P(x) is given as:

P"(x) = -1/15 < 0 This means that the maximum profit is at x = 3225. Hence:

P(3225) =  -(3225)²/30 + 215(3225) - 74000 = $272687.5

The money to be charge for each set is:

p(x) = 300 - 3225/30 = $192.5 per set

When taxed $5, the maximum profit is $272687.5

Answer 2

Answer:

b) $289000 profit,3300 set, $190 per set


Related Questions

please assist me with this problem: part 10​

Answers

Answer:

c

Step-by-step explanation:

Given

sinN = [tex]\frac{a}{b}[/tex] ( multiply both sides by b ) , then

a = bsinN → (a)

And

sinM = [tex]\frac{a}{y}[/tex] ( multiply both sides by y ), then

a = ysinM → (b)

Thus a is both (a) and (b)

HELP!!!!!!!!!! AP CALCULUS AB

Answers

Answer:

[tex]\lim_{x \to 5^{-}} f(x)= 54[/tex]

[tex]\lim_{x \to 5^{+}} f(x) = -17[/tex]

Step-by-step explanation:

+ means we are approaching from the right

- means we are approaching from the left

We are given that if x < 5, it is x² + 5x + 4

So to find [tex]\lim_{x \to 5^{-}} f(x)[/tex] we would plug in 5 into that piecewise function part:

5² + 5(5) + 4 = 54

We would be approaching y = 54 if we approach from the left.

We are given that x > 5, it is -4x + 3

So to find [tex]\lim_{x \to 5^{+}} f(x)[/tex] we would plug in 5 into that piecewise function part:

-4(5) + 3 = -17

We would approach y = -17 if we approached from the right.

Answer:

[tex]\lim_{x \to 5^-}f(x)=54\\\lim_{x \to 5^+}f(x)=-17[/tex]

Step-by-step explanation:

So, we have the function:

[tex]f(x)=x^2+5x+4,x<5\\f(x)=8,x=5\\f(x)=-4x+3,\text{ otherwise}[/tex]

And we want to show that this has a jump discontinuity.

As directed, calculate the limit at x=5 from the left and from the right. Thus:

[tex]\lim_{x \to 5^-}f(x)[/tex]

To calculate this, since we're coming from the left, x is less than 5. So, use the first equation:

[tex]\lim_{x \to 5^-}f(x)\\= \lim_{x \to 5^-}(x^2+5x+4)\\[/tex]

Use direct substitution:

[tex]=(5)^2+5(5)+4\\=25+25+4\\=54[/tex]

Thus, as the limit approaches f(5) from the left, the function approaches 54.

Now, calculate the limit at x=5 from the right. Since we're coming from the right, use the third equation:

[tex]\lim_{x \to 5^+}f(x)\\= \lim_{x \to 5^+}(-4x+3)[/tex]

Direct substitution:

[tex](-4(5)+3)\\=-20+3\\=-17[/tex]

Thus, as the limit approaches f(5) from the right, the function approaches -17.

As you can picture, there's a huge gap between y=54 and y=-17. The limits are not equal and both of the limits do exist. Thus, we have jump discontinuity.

Find the area to the nearest square foot of the shaded region below, consisting of a square with a circle cut out of it. Use 3.14 as an approximation for π. Need this ASAP

Answers

Answer:

22 square feet

Step-by-step explanation:

Area of shaded region = Area of square - Area of circle. The diameter of the circle is also the length of the side of the square as the circumference of the circle is on the circumference of the square.

Area of circle = 3.14 × r × r

r = 10 ÷ 2

= 5

Area of circle = 3.14 × 5 × 5

= 78.5

Area of square = length × length

Area of square = 10 × 10

= 100

Area of shaded region = Square - Circle

= 100 - 78.5

= 21.5

= 22 (to the nearest square foot)

I hope this helps :)

The park wanted to put up a new 500 foot fence around the rectangular playground. The length of the fence is going to be 100 foot. what will be the with of the fence?

Answers

Answer:

150 feet

Step-by-step explanation:

A rectangle has 2 pairs of equal sides.

One of the sides is 100 feet, meaning another side is 100 feet.

If we subtract 200 feet we are left with 300, which are the last two sides.

Divide 300 by 2 to get each side length.

150 feet

simplify the algebraic expression 3xy+5x+2+3y+x+4

Answers

Answer:

3xy+6x+3y+6

Step-by-step explanation:

You just need to combine like terms.

5x and x are like terms so you can add them to 6x.

2 and 4 are like terms so you can add them to 6

Help it’s not b what is the answer plz help

Answers

Answer:

c

Step-by-step explanation:

Please see attached picture for full solution.

1 and 2/3 plus 3 and 3/4
2 and 1/5 plus 3 and 7/8
4 and 1/2 plus 2 5/7
3/4 plus 2/3 plus 1/5

anyone?
URGENT
75 points!!

Answers

Answer:

Step-by-step explanation:

1  2/3  + 3 3/4 = 1  8/12 + 3  9/12 = 4 17/12 = 5 5/12

4 1/2 + 2 5/7 = 4 7/14 + 2 10/14 = 6 17/14 = 7 3/14

3/4 + 2/3 + 1/5 = 45/60 + 40/60 + 12/60 = 97/60 = 1 37/60

Answer:

Step-by-step explanation:

boom  = 1 37/60

for what values of x will 4^x be greater than 1 ?

Answers

Answer:

x>0

Step-by-step explanation:

We want to solve for x in the inequality:

4^x > 1

ln(4^x)=xln(4) > ln(1)=0

x > 0/ln(4) =0

x>0

So for any value of x greater than 0, you will have 4^x be greater than 1.

Pleaseeeeeeee helpppp

Answers

Answer:

  point G

Step-by-step explanation:

Find the referenced points on the diagram and notice the lines between them. The point at the intersection of those lines is what is wanted.

It is point G.

A solid sphere is cut into 10 equal wedges. The volume of each wedge is Solve the formula for r. 15 O Ar= V2 O B. r = 151 O c. r= 15V (27) O D. r= 15V - 27​

Answers

Answer:

A.  r = ∛ 15V / 2π

Step-by-step explanation:

Volume of a sphere = 4/3 π r³    

And to be divided into 10 equal wedges parts.

Volume of each wedge = V = 2/15 π r³

find r

V = 2 π r³ / 15

15 V = 2 π r³

15V / 2π = r³

r = ∛ 15V / 2π

The correct option will be option A i.e., r = [tex]\sqrt[3]{\frac{15}{2\pi } }[/tex]

It is given that a solid sphere is cut into 10 equal wedges , with each wedge having volume V = [tex]\frac{2}{15} \pi r^{3}[/tex]

We have to solve it to get the value of radius r.

What is the formula for volume of sphere ?

The volume of sphere is given by V = [tex]\frac{4}{3} \pi r^{3}[/tex] where , r is the radius of the sphere.

As per the question ;

Volume of sphere =  [tex]\frac{4}{3} \pi r^{3}[/tex]

To be divided into 10 equal wedges ;

Volume of each wedge of sphere will be ;

V = [tex]\frac{2}{15} \pi r^{3}[/tex]

15 V = 2[tex]\pi r^{3}[/tex]

or

r³ = [tex]\frac{15V}{2\pi }[/tex]

or

r = [tex]\sqrt[3]{\frac{15}{2\pi } }[/tex]

Thus , the correct option will be option A i.e., r = [tex]\sqrt[3]{\frac{15}{2\pi } }[/tex]

To learn more about volume of sphere click here ;

https://brainly.com/question/22807400

#SPJ2

PLEASE HELP !

Expand the following numbers ;

1.) 1.23 x 10^0

2.) 1.54 x 10^4

3.) 2.5 x 10^-3

4.) 5.67 x 10^-1

5.) 1.00 x 10^8

6.) 1.00 x 10^-8

Answers

Answer:

1. 1.23

2. 15400

3. 0.0025

4. 0.567

5. 100000000

6. 0.00000001

Step-by-step explanation:

you just move the decimal point left for negative and right for positive

1) 1.23 x 1 = 1.23
(Anything to the power of 0 = 1)

2) 1.54 x 10000 = 15400

3) 2.5 x 0.001 = 0.0025

4) 5.67 x 0.1 = 0.567

5) 1 x 100000000 = 100000000

6) 1 x 0.00000001 = 0.00000001

Two pieces of fabric
are 143/4 inches and
207/8 inches long. To
form a single piece in
length, 3/8 inch of
each masonry piece
was sewn together to
create a seam. What
is the final length of
the fabric after the
two pieces are sewn?

Answers

Answer:

            487/8 inches      

Step-by-step explanation:

[tex]\left(\dfrac{143}{4}-\dfrac38\right)+\left(\dfrac{207}{8}-\dfrac38\right)=\dfrac{286}{8}-\dfrac38+\dfrac{204}{8}=\dfrac{283}{8}+\dfrac{204}{8}=\dfrac{487}{8}[/tex]

Find the value of x in the equation below. 2x+8/6=1/3(x+4) A. x = 0 B. no real solutions C. infinitely many solutions D. x = 1

Answers

Answer:

x = 0

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

2*x+8/6-(1/3*(x+4))=0

Simplify 1/3

Equation at the end of step  1 :

(2x +  8/6) -  (1/3 * (x + 4))  = 0  

STEP  2 :

Equation at the end of step 2

 (2x + 8/6) -  (x+4)/3  = 0  

STEP  3 :  

Simplify 4/3

Equation at the end of step  3 :

(2x + 4/3) -  (x+4)/3  = 0  

STEP  4 :

Rewriting the whole as an Equivalent Fraction

Adding a fraction to a whole

Rewrite the whole as a fraction using  3  as the denominator :

2x =  2x/1  =  2x*3/3

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

2x * 3 + 4/3  =  6x+4/3

Equation at the end of step  4 :

(6x+4)/3 -  (x+4)/3  = 0  

STEP  5 :  Pulling out like terms

Pull out like factors :

6x + 4  =   2*(3x + 2)  

Adding fractions which have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

2*(3x+2)-((x+4))/3  =  5x/3

Equation at the end of step  5 :

5x/3 = 0  

STEP  6:  When a fraction equals zero

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now, to get rid of the denominator, multiply both sides of the equation by the denominator.

Here's how:

5x/3*3 = 0*3

Now, on the left hand side, the 3 cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

5x  = 0

Solving a Single Variable Equation:

Solve  :    5x = 0  

Divide both sides of the equation by 5:

x = 0

Refer to the sample data for​ pre-employment drug screening shown below. If one of the subjects is randomly​ selected, what is the probability that the test result is a false​ positive? Who would suffer from a false positive​ result? Why?
Pre-Employment Drug Screening Results
Positive test result Negative test result
Drug Use Is Indicated Drug Use Is Not Indicated
Subject Uses Drugs 38 12
Subject Is Not a drug user 19 29

Answers

Answer:

0.193877

Step-by-step explanation:

The data given to us is

Pre-Employment Drug Screening Results

                    Positive test result                 Negative test result

                    Drug Use Is Indicated            Drug Use Is Not Indicated

Subject Uses Drugs:            38                                         12

Subject Is Not a drug user: 19                                         29

Now the total of this is = 38+19+12+29= 98

Now the probability of false positive is = 19/98= 0.193877

The Subject Is Not a drug user  would suffer from a false positive. He is not a user and has a positive result.

in abc the measure of side c is 3.9cm if def has a dilation of abc with a scale factor of 2.5

Answers

Complete Question:

In ABC, the measure of sides c is 3.9 cm If DEF is a dilation ABC with a scale factor of 2.5 what is the measure of side f

Answer:

f = 9.75

Step-by-step Explanation:

From the information given, a sketch of ∆ABC and ∆DEF with their corresponding sides and angles have been attached below.

∆DEF is a dilation of ∆ABC, which is said to be on a scale factor of 2.5.

The scale factor is a whole number, this implies that ∆DEF is an enlargement of ∆ABC.

Since side c = 3.9 cm, in ∆ABC corresponds to side f, in ∆DEF, therefore, the measure of f would be:

f = measure of c × scale factor

f = 3.9 cm × 2.5

f = 9.75

Find an equation of the line passing through the points (−8,2) with the slope m= 4/3

Answers

Answer:

[tex]y=\frac{4}{3}x+\frac{38}{3}[/tex]

Step-by-step explanation:

So we want to find an equation of a line passing through (-8,2) with a slope of 4/3.

To do so, we can use the point-slope form. This is:

[tex]y-y_1=m(x-x_1)[/tex]

So, substitute (-8,2) for x₁ and y₁, and let m be 4/3:

[tex]y-2=\frac{4}{3}(x+8)[/tex]

Distribute the right:

[tex]y-2=\frac{4}{3}x+\frac{32}{3}[/tex]

Add 2 to both sides. Note that 2 can be written as 6/3. Thus:

[tex]y=\frac{4}{3}x+\frac{32}{3}+\frac{6}{3}[/tex]

Simplify:

[tex]y=\frac{4}{3}x+\frac{38}{3}[/tex]

And this is our equation :)

No sé cómo hacerlo. Y me gustaría que me ayudaran con él proceso?

Answers

Answer:

BC=11

Step-by-step explanation:

we need to find BC

and we  know that

AB= x+2

AC=13

BC=2x+11

A, B and C are collinear

that means that

AB+BC=AC

x+2+2x+11=13

3x+13=13

3x=0

x=0

so BC=2(0)+11

BC=11

a company has $25,000 in cash. next month the company anticipates sales revenue of $10,000, equiptment expense of $2,500, insurance costs of $100, and $200 in licensing fees. what is the projected cash flow at the end of the month?

Answers

Answer:o

Step-by-step explanation:

Round 7/12 to the nearest hundredth

Answers

Answer:

7.00

Step-by-step explanation:

so you have to round to the narest 0.01 the easy way to do it is round to the hundreth place. And you will get your answer which is 7.00

for stella’s lemonade recipe, 18 lemons are required to make 15 cups of lemonade. at what rate are lemons being used in cups of lemonade per lemon? express your answer in simplest form.

Answers

Answer:

  5/6 cups/lemon

Step-by-step explanation:

(15 cups)/(18 lemons) = (15/18) cups/lemon = 5/6 cups/lemon

Ben can type 25 words in half a minute at the rate how many words can he type in 5 minutes

Answers

Answer: 250 words in 5 minutes

Step-by-step explanation:

250 Words In 5 Minutes Would Be Your answer

Let
f(x) =

7x − 5, x ≤ −5
−x2, x > −5
.
Find
f(−1), f(−5), and f(−6)

Answers

Answer:

EZ

Step-by-step explanation:

EZ

7) A jet travels 440 miles in 2 hours. At this rate, how far could the jet Hy
12 hours? What is the rate of speed of the jet?

Answers

Answer:

2,640 miles in 12 hours.

Step-by-step explanation:

440/2=220mph

220*12 hours=2,640

rate of speed=220pmh

440 divided by two is 220
So 220 mph

What’s 2 1/6 - 1 5/6?

Answers

Answer:

2/6 or 1/3

Step-by-step explanation:

20 POINTSS!! Choose the fraction(s) equivalent to the given fraction. -1/7 Select all that apply A. -1/7 B. 1/-7 C. 1/7 D. -1/-7

Answers

Answer:

A and B.

Step-by-step explanation:

So we want to select the fractions that equal -1/7.

Let's go through each of the answer choices.

A)

A is -1/7, the exact same.

A is correct.

B)

B is 1/-7.

We can move the negative to the top.

So, 1/-7 is equivalent to -1/7.

B is also correct.

C)

C is 1/7

There are no negatives whatsoever.

C is not correct.

D)

We have -1/-7.

Again, move the negative to the top. We will have:

-(-1)/7

The two negatives cancel:

=1/7.

So, D is not correct.

Our answers are A and B.

The sum of the sequence of 685+678+671+664+...+6

Answers

Answer:

Sum of the sequence (Sn) = 33,859

Step-by-step explanation:

Given:

Sequence = 685+678+671+664+...+6

Find:

Sum of the sequence (Sn)

Computation:

a = 685

d = 678 - 985 = -7

an = 6

an = a+(n-1)d

6 = 685+(n-1)(-7)

-679 = (n-1)(-7)

97 = n-1

n = 98

So,

Sum of the sequence (Sn) = (n/2)[a+an]

Sum of the sequence (Sn) = (98/2)[685+6]

Sum of the sequence (Sn) = (49)(691)

Sum of the sequence (Sn) = 33,859

At a sporting goods store, Franklin tennis racquets normally sell for $110, but this week
they're selling for less than their normal price, How much has the price on each
d'acquet been lowered?

Answers

You need to specify what it was lowered too and what form of number do you want. Decimal? Percentage? Fraction?

6x- 10=-8+3x
Solve the linear equation.

Answers

Answer:

x =2/3

Step-by-step explanation:

[tex]6x-10=-8+3x\\\\\mathrm{Add\:}10\mathrm{\:to\:both\:sides}\\6x-10+10=-8+3x+10\\\\\mathrm{Simplify}\\6x=3x+2\\\\\mathrm{Subtract\:}3x\mathrm{\:from\:both\:sides}\\6x-3x=3x+2-3x\\\\Simplify\\3x=2\\\\\mathrm{Divide\:both\:sides\:by\:}3\\\frac{3x}{3}=\frac{2}{3}\\\\Simplify\\x=\frac{2}{3}[/tex]

Answer:

x = 2/3

Step-by-step explanation:

This equation can be solved by using conventional algebraic techniques.

We firstly want to make sure to get our constants on one side of the equation and then get our variables on the other.

6x - 10 = -8 + 3x Subtract 3x from both sides of the equation.

3x - 10 = -8 Add 10 to both sides of the equation.

3x = 2 Divide by 3 on both sides of the equation.

x = 2/3

Then, you can voluntarily check your answer.

6(2/3) - 10 = -8 + 3(2/3)

4 - 10 = -8 + 2

-6 = -6

There are 180 girls in a mixed school. if the ratio of girls to Boyd is 4:3,find the total number of students in the school. ​

Answers

Step 1) Set up a proportion

180 girls / x boys = 4 girls / 3 boys

540 = 4x

x = 135 boys

Step 2) Add the number of boys and girls together

180 + 135 = 315

Answer: 315 total students

What is the answer rounded to the nearest whole number

Answers

you did to provide numbers for me to answer that
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