Write the equation of a line with a slope of 1 that goes through the point (0,0).

If C(x) is the cost of producing x units of a commodity, then the average cost per unit is c(x) = C(x)/x. Consider the cost func

nadya68 [22]

Answer:

a) C(1,000)=288,491.11 $

b) c(1,000)=288.49 $/u

c) dC/dx(1,000)=349.74 $/u

d) x=100 u

e) c=220 $/u

Step-by-step explanation:

(a) Find the total cost at a production level of 1000 units.

$C(x) = 2,000 + 160x + 4x^{3/2}\\\\C(1,000)=2,000 + 160(1,000) + 4(1,000)^{3/2}\\\\C(1,000)=2,000+160,000+126,491.11= 288,491.11$

(b) Find the average cost at a production level of 1000 units.

$c(x)=C(x)/x\\\\c(1,000)=C(1,000)/1,000=288,491.11/1,000=288.49$

(c) Find the marginal cost at a production level of 1000 units.

$\frac{dC}{dx} =0+160+4*(3/2)x^{3/2-1}=160+6x^{1/2}\\\\dC/dx|_{1,000}=160+6*(1,000)^{1/2}=160+189.74=349.74$

(d) Find the production level that will minimize the average cost.

$c=2,000x^{-1}+160+4x^{1/2}\\\\dc/dx=2,000(-1)x^{-2}+0+4(1/2)x^{-1/2}=0\\\\-2,000x^{-2}+2x^{-1/2}=0\\\\2x^{-1/2}=2,000x^{-2}\\\\x^{-1/2+2}=1,000\\\\x^{3/2}=1,000\\\\x=1,000^{2/3}=100$

(e) What is the minimum average cost?

$c(x) = 2,000/x + 160 + 4x^{1/2}\\\\C(100)=2,000/100 + 160 + 4(100)^{1/2}=20+160+40=220$

5 0

3 years ago

6. If four numbers are in proportion, then the terms equals the product of<br>

snow_tiger [21]

Answer: If four numbers are proportional, a : b = c : d, then the product of the extremes is equal to the product of the means. ad = bc

3 0

2 years ago

How much paint does Brielle need to finish her room

KATRIN_1 [288]

Answer:

Paint Needed = 1.25 gallons = It means 1 gallon and 1 quart of paint is needed to paint the Briellie's room.

Step-by-step explanation:

As, this question is incomplete, so we will create similar question and complete it. '

Let's suppose Brielle's room has following dimensions:

Length of two walls = 10 ft

Length of other two walls = 12 ft

Height of the room from bottom to ceiling = 10 ft

In order to calculate the amount of paint needed, we need to calculate the surface area of the room to be painted.

So, for that, add all the lengths together and multiply it by height of the room.

SF = (L1 +L2 +L3+ L4) x H

SF = (10 + 10 + 12 + 12) x (10)

SF = 440 sq.ft = Actual footage of the room to be painted.

Now, we have convert this number in gallons to know the amount of paint required to paint Brielle's room. For this, we need to divide our SF to 350 sq.ft per gallon.

Paint Needed = 440 sq.ft / 350 sq.ft per gallon

Paint Needed = 1.25 gallons = It means 1 gallon and 1 quart of paint is needed to paint the Briellie's room.

4 0

3 years ago

two families go to a basketball game one family purchases two adult tickets and 3 youth tickets for $33 another family purchases

miskamm [114]

67,5 $ for 2 youth tickets and 5 adult tickets

6 0

3 years ago

PLEASE HELP! DUE TODAY :))

Aleonysh [2.5K]

Step-by-step explanation:

do like the picture I sent

3 0

3 years ago