i really need help

Question

A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. Using this equation, find out the maximum amount of profit the company can make, to the nearest dollar. y=12x^2+718x-5419

Answer 1

probably a misprint

as written an infinite price gives the highest profit

change/correct one sign, then

y'=24x-718=0

x=718/24=359/12

max profit= 12(359/12)^2-718(359/12)-5419

= 1,546,572-26,899.1666...

=about $1,519,672.83

or more change the problem, with -12x^2, not +12x^2 to

y=-12x^2+718x-5419

then

-24x+718=0

gives same answer: about one and half million dollars

Profit = Revenue - Cost

y= R-C = 12x^2-178x - 5419

where R = 12x^2, C =178x +5419, variable cost =178x, fixed cost =5419

or a similar interpretation