A store owner estimates that by charging x dollars each for a certain lamp, he can sell 25 - x lamps each week. What price will yield maximum revenue?

Answer:[tex]\frac{25}{2}[/tex] or 12.5Step-by-step explanation:So if 25 - x items are sold, and they each cost x, we can write an equation for the revenue to be y = (25 - x)xThe vertex of this equation will represent the maximum revenue.  So we need to write this equation in vertex form so we can find the vertex. Vertex from is y = a(x - h)^2+ k,where (h,k) represent the vertex.the vertex form of this equation would be [tex]y= -(x-\frac{25}{2} )^{2} +\frac{625}{4}[/tex]And the vertex would be [tex](\frac{25}{2} ,\frac{625}{4})[/tex]This means the maximum revenue will occur when x = 25/2