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Bob owns a watch repair shop. have the lowest cost? operating his shop s given by C·2x2 He has found that the cost o 216x + 1 1 243 where C s the cost in dolars, and x s the number of watches repaired How many watches must he re r How many watches must he repair to have the lowest cost?

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Answer:

The number of watches must he repair to have the lowest cost is 54.

Explanation:

The cost of operating Bob's shop is given by


C(x)=2x^2-216x+11243

Differentiate the given function with respect to x.


C'(x)=2(2x)-216(1)+(0)


C'(x)=4x-216 ... (1)

Equate C'(x) equal to 0, to find the critical point.


0=4x-216


216=4x

Divide both sides by 4.


(216)/(4)=x


54=x

Differentiate C'(x) with respect to x.


C''(x)=4

C''(x)>0, it means the cost of operating is minimum at x=54.

Therefore the number of watches must he repair to have the lowest cost is 54.

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