The scale for the drawing of a rectangular playing field is 2 inches = 5 feet.

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

Felix earns $450 per week plus 3% of sales over $4800. Felix’s sales are $53000. How much does Felix earn?Felix earns $450 per w

kirill [66]

Answer:

<em>Felix earns total $594 per week.</em>

Step-by-step explanation:

Felix’s sales are $53000.

So, <u>the amount of sales over $4800 will be</u>: $\$53000-\$4800= \$48200$

Felix earns $450 per week and additional 3% of sales over $4800.

So, his additional income $= (\$4800\times 0.03)=\$144$

Thus, Felix's total income will be: $(\$450+\$144)=\$594$

3 0

4 years ago

What is the perimeter of the rectangle? one side is 6in. and the A=30 sq in.

monitta

The perimeter of a rectangle can be found by dividing the area by one side.
30/6=5
Then, add the sides up and you get the perimeter.
5+5+6+6=22

The answer is 22 inches.

3 0

4 years ago

Read 2 more answers

Segment AE is a median for Triangle ABC.

Shalnov [3]

Step-by-step explanation:

$BC = BE + CE...(\because B-E-C) \\ \\ \therefore \: BC = 3x - 5 + x + 1 \\ \\ \therefore \: BC = 4x - 4 \\ \\ \huge \red{ \boxed{ \therefore \: BC = 4(x - 1)}}$

4 0

4 years ago

The product of two consecutive positive integers is 1,332. Explain how you can write and solve a quadratic equation to find the

taurus [48]

Product of two consecutive integer so this mean that x and y but y = x+1 than

x(x+1)=1332

x^2 +x -1332 =0 so bc. you get 36*37=1332 and 37x-36x=x so you can rewriting this quadratic factorized completlie

x^2 +x -1332 = 0

(x+37)(x-36)=0

x+37=0

x=-37 so the larger integer result that will be 37

9 0

4 years ago

Read 2 more answers