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](https://tex.z-dn.net/?f=C%28x%29%20%3D%202%2C000%20%2B%20160x%20%2B%204x%5E%7B3%2F2%7D%5C%5C%5C%5CC%281%2C000%29%3D2%2C000%20%2B%20160%281%2C000%29%20%2B%204%281%2C000%29%5E%7B3%2F2%7D%5C%5C%5C%5CC%281%2C000%29%3D2%2C000%2B160%2C000%2B126%2C491.11%3D%20288%2C491.11)
(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](https://tex.z-dn.net/?f=c%28x%29%3DC%28x%29%2Fx%5C%5C%5C%5Cc%281%2C000%29%3DC%281%2C000%29%2F1%2C000%3D288%2C491.11%2F1%2C000%3D288.49)
(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](https://tex.z-dn.net/?f=%5Cfrac%7BdC%7D%7Bdx%7D%20%3D0%2B160%2B4%2A%283%2F2%29x%5E%7B3%2F2-1%7D%3D160%2B6x%5E%7B1%2F2%7D%5C%5C%5C%5CdC%2Fdx%7C_%7B1%2C000%7D%3D160%2B6%2A%281%2C000%29%5E%7B1%2F2%7D%3D160%2B189.74%3D349.74)
(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](https://tex.z-dn.net/?f=c%3D2%2C000x%5E%7B-1%7D%2B160%2B4x%5E%7B1%2F2%7D%5C%5C%5C%5Cdc%2Fdx%3D2%2C000%28-1%29x%5E%7B-2%7D%2B0%2B4%281%2F2%29x%5E%7B-1%2F2%7D%3D0%5C%5C%5C%5C-2%2C000x%5E%7B-2%7D%2B2x%5E%7B-1%2F2%7D%3D0%5C%5C%5C%5C2x%5E%7B-1%2F2%7D%3D2%2C000x%5E%7B-2%7D%5C%5C%5C%5Cx%5E%7B-1%2F2%2B2%7D%3D1%2C000%5C%5C%5C%5Cx%5E%7B3%2F2%7D%3D1%2C000%5C%5C%5C%5Cx%3D1%2C000%5E%7B2%2F3%7D%3D100)
(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](https://tex.z-dn.net/?f=c%28x%29%20%3D%202%2C000%2Fx%20%2B%20160%20%2B%204x%5E%7B1%2F2%7D%5C%5C%5C%5CC%28100%29%3D2%2C000%2F100%20%2B%20160%20%2B%204%28100%29%5E%7B1%2F2%7D%3D20%2B160%2B40%3D220)
You could find his score for those three games by subtracting -700 and 400 to get 1100.
Answer:
Can you do it in english? I can't read in spanish sorry.
The answer would be angles UVX and RSQ.
Hope this helps