Question

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?

Answer 1

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.