(-3) with a power of four is?

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

Tania purchased P packages of pasta for $1.25 each and J jars of sauce for $1.85 each. She purchased 22 items and spent $33.50.

sergey [27]

Answer:

you would need to first do

(p times 1.25)

+

(j times 1.85)

and then

22 divided by 33.50

Step-by-step explanation:

3 0

3 years ago

Please need help, Will give brainiest!!!!

timurjin [86]

I'd say its D but im not quite sure, its what makes most sense to me.

6 0

3 years ago

How do you factorise fully x³-x

Harman [31]

Answer:

=x³-x

=x(x²-1)

=x(x²-1²)

=x(x+1)(x-1)

hope it helps.

4 0

2 years ago

A pair of shoes is on sale for 32$. The original price was $48. What is the percentage decrease in this price?

Licemer1 [7]

The decrease rate is 33.3%
Solution : 32$ on sale , original price is 48%
The deceased rate is x
48 (1-X)=32
x= 0.333

6 0

3 years ago

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