For a certain company, the cost function for producing x items is C(x)=30x+150 and the revenue function for selling x items is R(x)=−0.5(x−90)2+4,050. The maximum capacity of the company is 130 items.
The profit function P(x) is the revenue function R(x) (how much it takes in) minus the cost function C(x) (how much it spends). In economic models, one typically assumes that a company wants to maximize its profit, or at least make a profit!



Answers to some of the questions are given below so that you can check your work.



Assuming that the company sells all that it produces, what is the profit function?
P(x)=
Preview Change entry mode .

Hint: Profit = Revenue - Cost as we examined in Discussion 3.

What is the domain of P(x)?
Hint: Does calculating P(x) make sense when x=−10 or x=1,000?

The company can choose to produce either 60 or 70 items. What is their profit for each case, and which level of production should they choose?
Profit when producing 60 items =
Number


Profit when producing 70 items =
Number


Can you explain, from our model, why the company makes less profit when producing 10 more units?

Answers

Answer 1

Profit, revenue and cost are related, and can be calculated from one another.

The profit function is [tex]\mathbf{P(x) =-0.5(x -90)^2 - 30x + 3900}[/tex]The domain of the profit function is x > 0The profit when producing 60 items is 1650The profit when producing 70 items is 1600

The cost function is given as:

[tex]\mathbf{C(x) =30x + 150}[/tex]

The revenue function is given as:

[tex]\mathbf{R(x) =-0.5(x -90)^2 + 4050}[/tex]

(a) Calculate the profit function

This is calculated using:

[tex]\mathbf{P(x) = R(x) - C(x)}[/tex]

So, we have:

[tex]\mathbf{P(x) =-0.5(x -90)^2 + 4050 - 30x - 150}[/tex]

Evaluate like terms

[tex]\mathbf{P(x) =-0.5(x -90)^2 - 30x + 3900}[/tex]

(b) The domain of the profit function

When profit is 0 or less, then it becomes no profit.

Hence, the domain of the profit function is x > 0

(c) The profit for 60 and 70 items

Substitute 60 and 70 for x in P(x)

[tex]\mathbf{P(60) =-0.5(60 -90)^2 - 30 \times 60 + 3900}[/tex]

[tex]\mathbf{P(60) =1650}[/tex]

The profit when producing 60 items is 1650

[tex]\mathbf{P(70) =-0.5(70 -90)^2 - 30 \times 70 + 3900}[/tex]

[tex]\mathbf{P(70) = 1500}[/tex]

The profit when producing 70 items is 1600

(d) Why producing 10 more units less profit

When a function reaches the optimal value, the value of the function begins to reduce.

This means that, producing 10 more units takes the profit function beyond its maximum point.

Read more about profit, cost and revenue at:

https://brainly.com/question/11384352


Related Questions

A A color printer prints 23 pages in 8 minutes.
How many minutes does it take per page?

Answers

Answer:

almost 3 pages

Step-by-step explanation:

take 23 divided by 8 =2.875

A radioactive substance decays exponentially. A scientist begins with 150 milligrams of a radioactive substance. After 20 hours, 75 mg of the substance remains. How many milligrams will remain after 27 hours?

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Answer:

Step-by-step explanation:

Hi, I got 8 points off on this problem, can you help me figure out what I did wrong?

Answers

Answer:

Possible errors: Triangle classification and definition.

Step-by-step explanation:

An isoceles triangle has at least two congruent sides of the same length.  

Given the triangle that has two equal angles, and that you'll have to prove that the triangle also has two equal sides.  

Using the Converse of Isoceles Triangle Theorem, where it states that if a triangle has two congruent angles < PQR ≅ < PRQ, for which opposite sides of those angles are congruent:  

The opposite side of <PQR is line PR.The opposite side of <PRQ is line PQ.  

Additionally, connecting point P to point X along the line QR such that PX ⊥ QR, divides △PQR into two symmetrical sections, where points Q and R are equidistant from point X.      

Answer:

Possible errors: Triangle classification and definition.

Given (x – 7)2 = 36, select the values of x.

x = 13

x = 1

x = –29

x = 42

Answers

Answer:

x = 13 and x = 1

Step-by-step explanation:

(x-7)² = 36

simplify left side of equation

x² - 14x + 49 = 36

Our object now is to get every thing on the left side of the equal sign so we can factor. To do this, we subtract 36 from both sides

x² - 14x + 13 = 0

we then factor the left side of the equation

( x - 1 ) ( x - 13 ) = 0

we then set factors equal to 0 and solve both factors for x

x - 1 = 0

add 1 to both sides

x = 1

x - 13 = 0

add 13 to both sides

x = 13

The values of x are x = 13 and x = 1

When 36x^4 + 12x^8 is divided by 12x^4, the result is

Answers

Answer:

The result is 3+x^4.

A grower packs 4,568 peaches. He packs the most peaches possible, dividing them equally into 9 boxes, and then gives away the remaining peaches.
How many peaches are in each box.
How many peaches does he give away.
If he sells 7 boxes, how many peaches does he have left.

Answers

507 peaches in each box.

He gives away 5 peaches.

If he sells 7 boxes he has 1019 peaches left.

Hope this helps.

507 peaches in each box

He gives away 5 peaches

If he’s sells 7 boxes he’ll have 1014 peaches left

Jack’s truck had used 30 gallons of fuel from a 50 gallon tank. What percentage was used? *

Answers

anwers: is 15 because I did 30 percent of 50

The answer is 60% because you can take the 50 and times it by 2 to get 100 and you can take the 30 and times it by to to get 60 so you know that 30 gallons out of a 50 gallon tank is 60% of the fuel

Which of the following is an equivalent form of the compound inequality

Answers

Answer:

pls mark brainy

Step-by-step explanation:

option (d) is correct.

An equivalent form of the  given compound inequality −44 > −2x − 8 ≥ −8 is  −44 > −2x − 8 and −2x − 8 ≥ −8

Step-by-step explanation:

Given a compound inequality −44 > −2x − 8 ≥ −8

We have to write  an equivalent form of compound inequality.

Compound inequality  consists of two inequalities joined together and the solution is the intersection of each inequality.

Compound inequality has two sides the left hand side and right hand side we can solve them by taking each inequality one at a time.

For given compound inequality, −44 > −2x − 8 ≥ −8

we have

Left side of inequality as  −44 > −2x − 8

and right side of inequality as  −2x − 8 ≥ −8

Thus, option (d) is correct.

Thus, An equivalent form of the  given compound inequality −44 > −2x − 8 ≥ −8 is  −44 > −2x − 8 and −2x − 8 ≥ −8

What is the domain of the square root function graphed below?
4
-6
4
-2
6
X
15
6

Answers

Answer:

x[tex]\leq[/tex]-1

Step-by-step explanation:

How do you know whether two quantities x and y are proportional?

Answers

Answer:

I did this question for my little brother. and the answer is A. I think.

how to make it guys please

Answers

Answer:

were is the qn?

Step-by-step explanation:

Find the shaded area

Answers

216-64=152

152 hope this helps!!

Answer:

30

Step-by-step explanation:

What is 64 minutes as mixed number? (i'm pretty sure it might be
[tex]1 \frac{?}{?} [/tex]
but i don't know)

Answers

Answer:

1 1/15

Step-by-step explanation:

64 minutes is the same thing as 64/60 minutes.

64 goes into 60 once. 64-60=4, so that would be your numerator. You would keep the denominator as 60, since it's still out of 60.

If you put those numbers together your fraction would be

1 and 4/60, if you want to simplify, 60/4=15, so 1 and 1/15 would be your fraction.

Hope this helped!

Use the Pythagorean Theorem to find the missing length and
then round the result to the nearest tenth.
a = 12, b = 12, C =

Answers

Step-by-step explanation:

c = 12√2. or 16.968.

hope this helps you.

Since both a & b have the same measurements, the triangle is a right angled isosceles triangle (we use pythagorean theorem only for right angled triangles). So, C is obviously the hypotenuse of the triangle (the longest side).

According to the pythagorean theorem,

Hypotenuse² = Base² + Altitude²

C² = A² + B²

C² = 12² + 12²

C² = 144 + 144

C² = 288

C = √288

C = 16.975

C = 17 (approx.)

______

RainbowSalt2222 ☔

I need help!!! Answer asap plz
A number cube will be rolled 100 times as part of an experiment. Which calculation would you use to predict the number of times a 4 will be rolled?
A. (36)(1/4)
B. (100)(1/4)
C. (100)(1/6)
D. (36)(1/4)
No links please

Answers

C, because you roll 100 times, and you want to find out how many times you got the number 4. This may make it seem like you should use 1/4. However, 4 is only one number out of the six possible numbers. Therefore, c is correct
A & D, as its to my understanding, you’ve put the same answer for the two. therefor it could be either

What is the solution of the system of equations?

Answers

your desmos graph is really weird as the point is between 4 and 8 but with the one y=-x+5 we can see that the y intercept is 5 and the x value is 0

so the point is 0,5

Please help me with this problem

Answers

Hello this will be easy for you.

Look at the picture, you have the angle UTR which is of 90° degrees. Thus the angle UTS is also 90° .

But the sum of the angles of a triangle is by property equal to 180° so the angle UVT must be equal to 180-90-64 = 26°.

Now we are getting near to solve that x+8 degrees angle.

Recall that UVT is 26° ok ? So 180-26 = x+8

Thus

x+8 = 154

x = 154 - 8

x = 146

Finally the angle UVS = 154 and the value of x = 146

You can see all the angles in the image attached below

Good luck you will be the best

Which expression is equivalent to 125 in expressional form

FAST PLS

Answers

Start by prime factorising 125.

125 = 5 × 5 × 5

If you check the given options, the correct answer is :-

5³ (3rd option)

Verification:-

5³ = 5 × 5 × 5 = 125

Note :-

The 2nd option also gives 125, but they've asked for the answer in exponential form, so the 3rd option is the correct one.

________

꧁✿ ᴿᴬᴵᴺᴮᴼᵂˢᴬᴸᵀ2222 ✬꧂

Option c- 5 raised to power of 3

Just number three pls give right answer and will give brainless

Answers

Answer:

i think 34

Step-by-step explanation:

because thats the answer i got on calculator

What is the measure of angle 1

Answers

The answer is 88 degrees

Angle 1= 88 degrees
( the third option )

Situation. 11. The weather channel reported overnight rainfall of 1.5 inches and an average of 0.5 inches each hour for the remainder of the day. After how many hours will there be more than 5 inches of rain?​

Answers

Answer: The amount of precipitation that falls around the world may range from less than 0.1 inch per year in some deserts to more than 900 inches per year

Step-by-step explanation:

What is: 17/21 + 1/3 - 5/7 as a fraction in simplest form?

(Giving brainliest, 5 stars and a thanks)

Answers

Answer:

3/7

Step-by-step explanation:

it is -1/21 as a fraction

Help help help help please please e

Answers

The answer, when rounded to the nearest tenth is 19.2

First you can get rid of the decimals by multiplying both numbers by 100, this just makes the whole problem easier. Now all that needs to be done is long division:

(In my work I didn’t realize that it said round to the nearest tenth until I had already gotten past what I needed to find)

the table shows the pricing for four different types of gasoline which type cost the least per gallon a $20.20 for 10 galb $26.04 for 12 gal c $28.14 for 14 gal d $30.45 for 15 gal​

Answers

Answer:

A is the cheapest deal.

Step-by-step explanation:

find unit rate; cost / quantity

20.20 / 10 = $2.02 per gallon

26.04 / 12 = $2.17 per gallon

28.24 / 24 = $2.01 per gallon

30.45 / 25 = $2.03 per gallon

I know that x + 2 is a factor of P(x) = 2x^{3} + 5x^{2} + 5x + 6, but I just don't know how to do the second half

Answers

Answer:

explain it again

Step-by-step explanation:

i don't understand

A store pays $79 for a desk and marks the price up by 10%. What is the new price?​

Answers

The new price would be $86.9

Answer: 86.90$

Step-by-step explanation:

10/79=7.90$. 7.90$ + 79.00$= 86.90$

A board that measures 3/4 feet long is cut into 6 equal pieces. What is the length of each piece?

Answers

Answer:

See below:

Step-by-step explanation:

So we know that there is a [tex]\frac{3}{4}[/tex] feet long board and that it is split into 6 pieces.

With that information, we can split it by doing the following:

1. [tex]\frac{3}{4} *\frac{1}{6}[/tex]

We can do this because we have a board that is 0.75 feet long and we multiply it by one sixth because we want to divide a fraction and to do that we have to flip the fraction.

After doing that, we get our answer of [tex]\frac{3}{24}=\frac{1}{8}[/tex]

This means that each piece is [tex]\frac{1}{8}[/tex] feet long.

Cheers!

Answer:

3/24 feet long each.

Step-by-step explanation:

You are dividing 3/4 by 6, so the expression is:

(3/4) / 6

You can rewrite this as:

(3/4) * (1/6)

Then, multiply across, with the numerator of the new fraction being (3 * 1) and the denominator being (4 * 6)

Your answer becomes 3/24

Jacob followed a recipe that requires 2 cups of water for ever 3 cups of flour. If he used 8 cups of flour, how many cups of water did he use?

options

2 2/3

4


5 1/3

12

Answers

Answer:12

Step-by-step explanation:

3 divided by 2 = 1.5

1.5x8=12

He used 12 cups of water

Have A Good Day

Five students wrote a quiz with the maximum score of 50. The scores of four of the students are 42,43,46 and 49. The score of the fifth student was N. The mean of the five students' scores was the same as the median of the five students' scores . What is the possible values of N .​

Answers

Answer:

45

Step-by-step explanation:

avg=42+43+46+49/4

avg=180/4

n=45

In circle O, what is mArc A E?

Answers

Answer:

Step-by-step explanation:

By using the theorem of secants intersecting externally, Measure of angle formed by two secants, from a point outside the circle is half the difference of the measures of the intercepted arcs. m∠C =. 36° =. 72° = °. …

By using the theorem of secants intersecting externally, Measure of angle formed by two secants, from a point outside the circle is half the difference of the measures of the intercepted arcs. m∠C =. 36° =. 72° = °. …

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