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
ludmilkaskok [199]
3 years ago
15

Given the Production Function Q = 72X + 15X 2 - X 3 , where Q =Output and X=Input (5 marks) a) What is the Marginal Product (MP)

when X = 8? B) What is the Average Product (AP) when X = 6? C) At what value of X will Q be at its maximum? D) At what value of X will Diminishing Returns set in?
Mathematics
1 answer:
rusak2 [61]3 years ago
3 0

Answer:

a.) Marginal Product (MP) = 120

b.) Average Product = 126

c.) At x = 12, the output is maximum.

d.) After 5 levels of inputs diminishing returns set in.

Step-by-step explanation:

Given that,

Q = 72x + 15x² - x³

a.)

Marginal Product is equal to

\frac{dQ}{dx} = 72 + 30x - 3x^{2}

At x = 8

MP = 72 + 30(8) - 3(8)²

     = 72 + 240 - 192

     = 120

∴ we get

Marginal Product (MP) = 120

b.)

Average Product is equals to

= \frac{Q}{x}

= 72 + 15x - x²

At x = 6

Average Product = 72 + 15(6) - 6²

                             = 72 + 90 - 36

                             = 126

∴ we get

Average Product = 126

c.)

For Maximizing Q,

Put \frac{dQ}{dx} = 0

⇒72 + 30x - 3x² = 0

⇒24 + 10x - x² = 0

⇒x² - 10x - 24 = 0

⇒x² - 12x + 2x - 24 = 0

⇒x(x - 12) + 2(x - 12) = 0

⇒(x + 2)(x - 12) = 0

⇒x = -2, 12

As items can not be negative

∴ we get

At x = 12, the output is maximum.

d.)

Now,

For Diminishing Return

\frac{d(MP)}{dx} = \frac{d^{2}Q}{dx^{2} }   < 0

⇒30 - 6x < 0

⇒-6x < -30

⇒6x > 30

⇒x > 5

∴ we get

For x > 5, the diminishing returns set in

i.e.

After 5 levels of inputs diminishing returns set in.

You might be interested in
Which property of multiplication is shown? 6 · 1 = 1 · 6
saw5 [17]

Answer: Commutative property of multiplication  

Step-by-step explanation: The problem 6 · 1 = 1 · 6 demonstrates the commutative property of multiplication.

In other words, the commutative property of multiplication says that changing the order of the factors does not change the product.  

So for example here, 6 · 1 is equal to 6 and 1 · 6 also equals 6.

Since 6 = 6, we can easily see that 6 · 1 must be equal to 1 · 6.

In more general terms, the commutative property of multiplication can be written as a · b = b · a where <em>a</em> and <em>b</em> are variables that can represent any numbers.

5 0
2 years ago
Read 2 more answers
Someone could help me with problem 3-76 (b) pls
kupik [55]

Answer:

ok so you see the equation at the top... you are going to "plug in" the number in the "in" row to get the "out number

Step-by-step explanation:

example

in: 4

-2(-4)+1

8+1

9

so for the out row under -4 you would put 9

-2(-3)+1

6+1

7

so for the out row under 3 you would put 7

5 0
3 years ago
Read 2 more answers
Create a budget that will allow you to save at least $100 by the end of October.
insens350 [35]

According to the updated budget, the net income should be at least $2100.

A budget is an estimated strategy for a certain timeframe, mostly one year. Additionally, projected material amounts, expenditures, liabilities, holdings, responsibilities, and working capital may be included.

The following list explains why the figures shown above are accurate:

The factors for the costs in the previous budget are;

Net income =$1,850.00

Cost of rent =$600

Gas, vehicle payment, and insurance together = $475.

Cost of phone, online world, and utility companies = $230.

Cost of grocery stores= $300

Cost of amusement= $50

Cost of homeowners insurance = $20.

$75 has been set aside for recreational expenditures.

Net monthly savings = $100.

Modifications to the spending plan:

$50 is the allotted sum for a computer system.

Monthly net savings = $300

∴Savings increases= $300-$100=$200

Previous net income+ cost of computer system+ 200(extra savings than previous)

= $(1850+50+200)

=$2100

So,Net earnings = $2,100

Learn more about the budget plan:

brainly.com/question/22057981?referrer=searchResults

#SPJ10

3 0
2 years ago
What is the Lateral area of this prism ?
Mazyrski [523]

Answer:

idk let me go look at it

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Can someone help me with this? please<br><br>alguien me puede ayudar con esto? porfavorr
soldi70 [24.7K]

See attachment for the number line that compares the numbers 5.3, 5 1/5 and 5

<h3>How to plot the numbers on the number line?</h3>

The numbers are given as:

5.3, 5 1/5 and 5

We start by representing the numbers as decimals (i.e. real numbers).

So, we have:

5.3, 5.2 and 5

Reorder the numbers in ascending number (i.e. from least to greatest)

So, we have

5, 5.2 and 5.3

Next, we plot the numbers on a number line using a scale of 0.1

This can be visualized as

5        5.2      5.3

See attachment for the number line that compares the numbers 5.3, 5 1/5 and 5

Read more about number line at

brainly.com/question/24644930

#SPJ1

8 0
2 years ago
Other questions:
  • Who prescribed the most medicine and why explain
    6·1 answer
  • What is the fraction in between 1/2&lt;, &lt;4/5
    12·1 answer
  • PLEASE HELP!
    6·2 answers
  • Round 90.2844097979 to 3 decimals
    10·1 answer
  • Is it the answer option D?
    14·2 answers
  • cooper's jump rope is for 4 2/5. luke's jump rope is 4 3/4 ft long. whose jump rope is longer? how much longer? show your work
    5·1 answer
  • This graph shows a proportional relationship.
    12·1 answer
  • The perimeter of a rectangle is 40cm. If the length were doubled and the width halved, the perimeter would be increased by 16cm.
    11·1 answer
  • In Triangle MNO, ∠N is 5 times the measure of ∠M, and∠O is 4 times the measure of ∠M.
    8·1 answer
  • Find 1 2··31 1 22 1··22. Show your work
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!