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 repair to have the lowest cost?
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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
{{{ graph( 300, 300, -50,100, -2000, 200, 2x^2-112x+58) }}}