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
[tex]C(x)=2x^2-216x+11243[/tex]
Differentiate the given function with respect to x.
[tex]C'(x)=2(2x)-216(1)+(0)[/tex]
[tex]C'(x)=4x-216[/tex] ... (1)
Equate C'(x) equal to 0, to find the critical point.
[tex]0=4x-216[/tex]
[tex]216=4x[/tex]
Divide both sides by 4.
[tex]\frac{216}{4}=x[/tex]
[tex]54=x[/tex]
Differentiate C'(x) with respect to x.
[tex]C''(x)=4[/tex]
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.
