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
Luden [163]
2 years ago
15

a manufacturer can produce a color pen at a cost of $3. the color pens have been selling for $5 per pen and at this price, consu

mers have been buying 4000 pens per month. the manufacturer is planning to raise the price of the pens and estimates that for each $1 increase in price, 400 fewer pens will be sold each month. at what price should the manufacturer sell the pen to maximize profit? what is the maximum profit?
Mathematics
1 answer:
Serjik [45]2 years ago
7 0
Let x be the number of increases of $1 a month.
Let y be the maximum profit.
The profit before the price increases:
$5-$3=$2
The profit when increasing the price:
y= (2+x x 1)(4000-400x)
y= 8000-800x +4000x -400x2             (x2: x square)
The vertex:
x= -3200/(-400 x 2) = 4
=> y= 14400
The price can maximize the profit is:
p= 3+ 2 +4x1= 9
The price can maximize the profit is $9
The maximum profit is $14400.
You might be interested in
In variables estimation sampling, the sample standard deviation is used to calculate the?
Nikitich [7]

The sample standard deviation is used to calculate the determine the spread of estimates for a set of observations (i.e., a data set) from the mean (average or expected value).

<h3>What is sample standard deviation?</h3>

The spread of a data distribution is measured by standard deviation. The average distance between each data point and the mean is measured.

The sample standard deviation (s) is a measurement of the variation from the expected values and is equal to the sample variance's square root.

where

s = sample standard deviation

N = the number of observations

xi= the observed values of a sample item

\overline {x}= the mean value of the observations

Learn more about simple standard deviation, refer:

brainly.com/question/26941429

#SPJ4

3 0
1 year ago
The length of a rectangle is 5 more than the width. Find the length and width of a rectangle if the area of the rectangle is 36
harkovskaia [24]

Answer:

width = 4 in

length = 9 in

Step-by-step explanation:

To solve this problem, write an expression for the length and use the area of a rectangle formula.

The formula for area of a triangle is A = lw

"A" is the area.

"l" is the length.

"w" is the width.

"The length of a rectangle is 5 more than the width". It is represented in an expression:

l = w + 5     The width plus 5 is the length.

We also know the area is 36 in². Using information we know, replace variables in the formula for area of a rectangle.

Substitute l = w + 5 and A = 36

A = lw

36 = (w + 5)w     Expand by multiplying w by the terms in the brackets.

36 = w² + 5w      Since the equation is quadratic, make it equate to 0.

36 - 36 = w² + 5w - 36   Subtract 36 from both sides

0 = w² + 5w - 36      Factor this. Use group factoring, which is when you replace the middle term (5w) with two terms that add to make 5w, and multiply to get the last term (-36).

0 = w² + 9w - 4w - 36      9w times -4w is -36. They also add to get 5w.

0 = (w² + 9w) + (-4w - 36)  Group the factors

0 = w(w + 9) + -4(w + 9)   Take out the common factor in each group.

0 = w(w + 9) + -4(w + 9)   Take out the new common factor binomial w+9

0 = (w + 9) (w - 4)    Fully factored equation.

w + 9 = 0       w - 4 = 0    Set each binomial to equal 0.

     w = -9            w = 4   Chose what makes sense to be the width.

The width cannot be a negative number, so the width is 4.

Since we know the width, we can find the length because the length is 5 more than the width.

l = w + 5

l = 4 + 5

l = 9      Length of the rectangle

Don't forget to include the units, inches.

Therefore the length is 9 inches and the width is 4 inches.

8 0
2 years ago
You buy a 1:1000 scale model of the Statue of Liberty during a trip to New York City. The height of the model is 9.3 centimeters
zalisa [80]
=9.3×1000
=9300cm
=9300÷100
=93m
5 0
3 years ago
Review the graph. On a coordinate plane, a function starts at (negative StartFraction pi Over 2 EndFraction, negative 1), has an
aivan3 [116]

Answer:

A

Step-by-step explanation:

4 0
2 years ago
An ostrich can run 174 feet in 3 seconds.
bonufazy [111]

Answer:

58 I think i'm wrong tho

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
Other questions:
  • Can someone please solve this problem?Quick!
    13·1 answer
  • Paul’s account balance is less than -$50. What is a possible balance for paul’s account? Explain.
    6·1 answer
  • Alyssa's company makes a profit of $175,000.
    15·1 answer
  • Round to the nearest thousandth 2.8151
    6·2 answers
  • Find the average rate of change for problems 1-3: X. X^2+7 2. 11 3. 16 4. 23 5. 32 6. 43 1) what is the average rate of change b
    5·1 answer
  • 17<br> Solve for x and round your answer to the Nearest Tenth.<br> 4 A<br> 6
    14·1 answer
  • A weatherman predicted 17 inches of snow. The town actually got 1 and 1/2 feet of snow. By what percent was the weatherman’s pre
    8·2 answers
  • Type your answer into the box,
    12·1 answer
  • I need help explaining this please .
    6·1 answer
  • A certain forest covers an area of 2000 km2. Suppose that each year this area decreases by 4.75%. What will the area be after 7
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!