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

Answer:

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

Step-by-step 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.

$\frac{216}{4}=x$

$54=x$

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.