Answer:
The number of additional vines to plant in order to maximize production is 200
The total number of vines to maximize production is 800
Step-by-step explanation:
Notice that the expression for the number of pounds of grapes per acre is in fact a quadratic expression in the variable "n":
which is clearly associated with a parabola with arms pointing down (negative coefficient in the variable "n" squared). So by finding the vertex of the parabola, we can give the answer to what "n" (number of additional vines to plant).
Recall that the vertex of a parabola of the general shape: has an x-component defined by:
then in our case, the "n" value for that vertex is:
Then the additional number of vines to maximize grape production is 200
So the total should be: 600 + 200 =800