SOLUTION: bOB OWN A WATCH REPAIR SHOP. hE HAS found that the cost of operating his shop is given by c(x) = 2x^2-112x+58, where c is cost and x is the number of watches repaired. how many wat

Question 689466: bOB OWN A WATCH REPAIR SHOP. hE HAS found that the cost of operating his shop is given by c(x) = 2x^2-112x+58, where c is cost and x is the number of watches repaired. how many watches must he repari to have the lowest cost?
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
bOB OWN A WATCH REPAIR SHOP. hE HAS found that the cost of operating his shop is given by c(x) = 2x^2-112x+58, where c is cost and x is the number of watches repaired. how many watches must he repair to have the lowest cost?
**
c(x) = 2x^2-112x+58
This is an equation of a parabola that opens upwards, (curve has a minimum)
Its standard form: y=A(x-h)^2+k, (h,k)=(x,y) coordinates of the vertex. (y-value is the minimum in this case.
c(x) = 2x^2-112x+58
complete the square
c(x)=2(x^2-56x+28^2)-2*28^2+58
c(x)=2(x^2-56x+784)-1568+58
c(x)=2(x-28)^2-1510
vertex: (28,-1510)
how many watches must he repair to have the lowest cost? 28
see graph below as a visual check

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