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
Vika [28.1K]
3 years ago
10

A company estimates that it can sell 3,000 units each month of its product if it prices each unit at $80. However, its monthly n

umber of sales will increase by 10 units for each $0.10 decrease in price. The company has fixed costs of $250. The cost to make each unit is $4.20. Find the level of production that maximizes the company's profit.
The Should Produce _________
Units at a price of $__________
Which will yield a profit of $_______
Mathematics
1 answer:
slamgirl [31]3 years ago
6 0

9514 1404 393

Answer:

  • 5290 units
  • $57.10 per unit
  • $279,591 profit

Step-by-step explanation:

For price p, the quantity q of units sold is said to be ...

  q = 3000 +10(80-p)/0.10 . . . . for price in dollars

Then the revenue will be ...

  r(p) = p·q = p(3000 +100(80-p)) = 100p(110 -p)

The cost is said to be ...

  c(q) = 250 +4.20q

  c(p) = 250 +4.20(100(110 -p)) = 250 +420(110 -p)

Then the profit function is ...

  P(p) = r(p) -c(p)

  P(p) = 100p(110 -p) -(250 +420(110 -p)) = (110 -p)(100p -420) -250

__

Ignoring the vertical offset of -250, the quadratic has zeros at 110 and 4.2. So, its line of symmetry (and vertex) will be found at ...

  p = (110 +4.2)/2 = 57.1 . . . . dollars per unit

The quantity that should be produced at that price is ...

  q(57.1) = 100(110 -57.1) = 5290 . . . . units produced

The profit at that price is ...

  P(57.1) = (110 -57.1)(100·57.1 -420) -250 = 52.9(5290) -250

  = $279,591 . . . . best profit

_____

<em>Additional comment</em>

After you have seen a few of these, you can write down the revenue function based on the rate of change of units sold.

If p is the price of a unit, then 80-p is the number of dollars of decrease in price for a price of p. Then (80 -p)/0.10 is the number of 10¢ decreases in price. The increase in units sold is 10 times this, or 10(80 -p)/0.10 = 100(80 -p). When that is added to 3000 units sold, the total is ...

  3000 +100(80 -p) = 3000 +8000 -100p

  = 11000 -100p = 100(110 -p) . . . . . quantity sold at price p

Revenue is the product of price times the number of units sold at that price.

Profit is the difference between revenue and cost.

You might be interested in
WILL GIVE BRAINLIEST ANSWER!!!
quester [9]

Answer:

everyone will have 15 dogs each

Step-by-step explanation:

dogs:

1+2+3+4+5=15

humans:

54+38+3+1+4=100

100x15=1500 <<<how many dogs there are in total

1500%100=15 <<<how many each person will get if u add all the dogs and divide them evenly for each person

3 0
2 years ago
Read 2 more answers
For a certain experiment, if we expect to get an apple 8 times in 200 trials, what is the theoretical probability of getting an
Maurinko [17]
The answer is C

If you divide 8 by 200 it becomes 0.04 which is 4/100 in fraction form. If you simplify it then become 1/25.
5 0
3 years ago
What is -5x + 2 equals negative 48
VikaD [51]
The answer would be X=10
First you would subtract 2 to -48 and that gives you -50. After you will divide the -5x to -50 and that gives you X=10

3 0
3 years ago
Read 2 more answers
Suppose you begin with a pile of n stones and split this pile into n piles of one stone each by successively splitting a pile of
rodikova [14]
Start with five stones
7 0
3 years ago
4x + 5y = 3 2x + 3y = 1Solve by elimination
Lesechka [4]

Answer:

The solution to the system of equations is:

x = 2, and y = -1

Explanation:

Given the pair of equations:

4x + 5y = 3 ..........................................................................(1)

2x + 3y = 1............................................................................(2)

To solve this by elimination:

Multiply equation (2) by 2, to eliminate x

Equation (2) becomes

4x + 6y = 2 .........................................................................(3)

Subtract equation (1) from (3)

4x - 4x + 6y - 5y = 2 - 3

y = -1 ....................................................................................(4)

Multiply equation (1) by 3 and equation (2) by 5 to eliminate y

Equation (1) becomes

12x + 15y = 9 .......................................................................(5)

Equation (2) becomes

10x + 15y = 5 ........................................................................(6)

Subtract equation (6) from (5)

12x - 10x + 15y - 15y = 9 - 5

2x = 4

Divide both sides by 2

x = 4/2 = 2 ............................................................................(7)

From equations (7) and (4)

x = 2, and y = -1

7 0
1 year ago
Other questions:
  • The banna is 8 inches longhow many 0.4 inces of banana can be cut from tis banna
    13·2 answers
  • ​françoise and maurice cut diagonally across a 30​-foot-by-120​-foot vacant rectangular lot on their way to school. how much dis
    8·1 answer
  • How do I work out this question?
    13·2 answers
  • Please help!!!!!!! Which of the following options is an equivalent function to f(x)=3(2)^3x
    15·2 answers
  • The Rockford's have a square play area that is built around a center sandbox that is in the shape of a circle. The sides of the
    13·1 answer
  • R^2+15r+56=0 <br> Quadratics factoring
    15·1 answer
  • What is the answer for this cause the answer I put is incorrect
    13·1 answer
  • Cuál es el problema actual que están viviendo los emprendedores?
    13·1 answer
  • I NEED HELP ASAP <br> FIND THE MEASURE OF MISSING ANGLE
    5·1 answer
  • If A(1,2), B(5,-4) and (-3,2) are the vertices of a triangle, which statement holds true?
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!