Question

Asked Nov 4, 2019

Assume that it costs a company approximately.

C(x) = 400,000 + 160x + 0.003x^{2}

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)

= $ 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** .

Step 3

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

Answer: Averag...

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