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]
2 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]2 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
Find the distance between the points given.<br><br> (0, -6) and (9, 6)
Leya [2.2K]
AB=9
AC=`12
BC=x=?
ABC is a triangle with 90 degree
x2=(9)2+(12)2
x2=81+144
x2=225
x=15 so the distance between the points given is 15
8 0
3 years ago
Read 2 more answers
Which equation shows the value of -2/5 - -9/15
Alika [10]

Answer:

D) 3/15

Step-by-step explanation:

(-2/5) - (-9/15) = (-6/15) - (-9/15) = (-6/15) + (9/15) = 3/15

6 0
2 years ago
The scatterplot shows the time it takes for a new hot plate to boil various amounts of water, and one lab group’s attempt at a l
Vera_Pavlovna [14]

so it will

be

E=>6^5 H2O 9^+7*8

7 0
3 years ago
Read 2 more answers
Plz some one look at this
aleksklad [387]
5 : - 1/6 = 0.167     out of 10 = 1.67  out of 100 = 16.7

even number  0.33 out of 10:-  3.3 out of 100:-  33

a prime number  0.5 out of 10: 5 and out of 100:- 50

multipl of 3:- 0/33  out of 10:- 3.3 and out of 100: 33
4 0
3 years ago
What is the surface area? 5 in 4 in 2 in
Dennis_Churaev [7]

I think the Answer is 76 in^2

Hope this helps

8 0
3 years ago
Other questions:
  • Sandra and her friend went to the candy store. Each of the purchased a bag of jelly beans. Sandra's bag weighed 1.25 pounds. Her
    14·2 answers
  • Please answer! Thank you! :)
    13·1 answer
  • I need an answer fast! Can somebody please help me???
    8·2 answers
  • A company made 4 million in the second quarter this is one third more than I made in the first quarter and forfeits of what I ma
    11·1 answer
  • an item is regularly priced at $41. it is on sale for 35% off the regular price. what is the sales price?
    5·1 answer
  • Which one is it pls help i dont understand
    15·2 answers
  • If x+y = 3, xy =2 what is the value of x‌3+y3​
    7·2 answers
  • True or false: The following table is linear.
    11·2 answers
  • 48 people attended the Sunday matinee to watch a film. .Three over 8 of the people went to see a romantic comedy. .One over six
    7·1 answer
  • Help Help Help HELPPP MEEE PLEASEE :&lt;
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!