You are building an addition to your

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)

rusak2 [61]

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.

3 0

3 years ago

Can u simplify 12.82817

ryzh [129]

Answer:

no

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

A snack company makes three batches of a nut mix using the recipe shown. Each batch contains a different total amount of mix.

stepladder [879]

Answer:

Batch 1: 3 cups cashews; Batch 2: 1/3 cup pistachios; Batch 3: 4/3 cups almonds and 2 cups cashews

Step-by-step explanation:

Let x represent the total amount of mix.

For Batch 1, we know that the amount of pistachios is 1/6 of the total and that is 1 cup; this gives us

1/6x = 1

Multiply both sides by 6:

1/6x(6) = 1(6)

x = 6

There are 6 cups total. 1/2 of the mix is cashews; this means 1/2(6) = 3 cups is cashews.

For Batch 2, we know that the amount of almonds is 1/3 of the total and that is 2/3 of a cup; this gives us

1/3x = 2/3

Multiply both sides by 3:

1/3x(3) = 2/3(3)

x = 6/3 = 2

There are 2 cups of mix total.

1/6 of the mix is pistachios; this gives us 1/6(2) = 2/6 = 1/3 cup pistachios.

For Batch 3, we know that the amount of pistachios is 1/6 of the total mix and that is 4/6 of a cup; this means

1/6x = 4/6

Multiply both sides by 6:

1/6x(6) = 4/6(6)

x = 24/6 = 4

There are 4 cups of mix total.

1/3 of the mix is almonds; this gives us 1/3(4) = 4/3 cups almonds.

1/2 of the mix is cashews; this gives us 1/2(4) = 2 cups cashews.

8 0

4 years ago

Read 2 more answers

Given that 2x – 2y = 23

lidiya [134]

Answer:

x = 41/2

Step-by-step explanation:

I am assuming that we are finding 'x' when y = 9.

$2x-2y=23\\\\2x-2(9)=23\\\\2x-18=23\\\\2x-18+18=23+18\\\\2x=41\\\\\frac{2x=41}{2}\\\\\boxed{x=\frac{41}{2}}$

Hope this helps!

8 0

3 years ago

Read 2 more answers

I need the answers to 7.

Mrrafil [7]

Answer: 8 22 7 13 from top to bottom

Step-by-step explanation:

On the first row, the number of 2-player games is 1 meaning 2 players are playing meaning 48 are left to play the 6-player games so 8 is the number

On the second, the number of 6-player games is 1 meaning 6 players are playing meaning 44 are left to play the 2-player games so 22 is the number

On the third, the number of 2-player games is 4 meaning 8 players are playing meaning 42 are left to play the 6-player games so 7 is the number

On the fourth, the number of 6-player games is 4 meaning 24 players are playing meaning 26 are left to play the 2-player games so 13 is the number

7 0

2 years ago