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Assume that it costs a company approximately. C(x) = 400,000 + 160x + 0.003x2dollars to manufacture x smartphones in an hour. (a) Find the marginal cost function. 160+.006x Use it to estimate how fast the cost is increasing when x = 10,000.$ per smartphoneCompare this with the exact cost of producing the 10,001st smartphone.The cost is increasing at a rate of $ per smartphone. The exact cost of producing the 10,001st smartphone is $ . Thus, there is a difference of $ . (b) Find the average cost function C and the average cost to produce the first 10,000 smartphones. C(x)= C(10,000)= $

Question

Asked Nov 4, 2019

Assume that it costs a company approximately.

C(x) = 400,000 + 160x + 0.003x²

dollars to manufacture x smartphones in an hour.

(a) Find the marginal cost function.

160+.006x

Use it to estimate how fast the cost is increasing when x = 10,000.

$ per smartphone

Compare this with the exact cost of producing the 10,001st smartphone.

The cost is increasing at a rate of $ per smartphone. The exact cost of producing the 10,001st smartphone is $ . Thus, there is a difference of $ .

(b) Find the average cost function C and the average cost to produce the first 10,000 smartphones.

C(x)=

C(10,000)

= $

Expert Answer

Step 1

C'(x)= 160+.006x

C'(10000)=160+.006(10000)=220

Answer: The cost is increasing by $220 per smart phone when x = 10,000.

Step 2

To find exact cost of 10,001 smartphone, we plug x=10001 in C(x).

The cost is increasing at a rate of $ 220 per smartphone. The exact cost of producing the 10,001st smartphone is $ 2300220 . Thus, there is a difference of $ 220 .

C(x) 400,000+160x+0.003x2
C(10001) 400,000+160(10001)+0.003(10001)
C(10001)-2300220 — Image Transcription
C(x) 400,000+160x+0.003x2 C(10001) 400,000+160(10001)+0.003(10001) C(10001)-2300220

Step 3

Average cost function c(x)= C(x)/x

Answer: Averag...

С()
с (x)%3D
х
400,000+160х+0.003x?
с(х)-
0.003x
160х
400000
с(х)-
X
х
400000
с(х)-
.+160+0.003х
X — Image Transcription
С() с (x)%3D х 400,000+160х+0.003x? с(х)- 0.003x 160х 400000 с(х)- X х 400000 с(х)- .+160+0.003х X

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