Agriculture At a certain vineyard it is found that each grape vine produces about 10 lb of grapes in a season when about 700 vines are planted per acre. For each additional vine that is planted, the production of each vine decreases by about 1 percent. So the number of pounds of grapes produced per acre is modeled by
where n is the number of additional vines planted. Find the number of vines that should be planted to maximize grape production.
To evaluate: The number of vines that should be planted to maximize the grape production.
Answer to Problem 70E
The number of vines that should be planted to maximize the grape production is
Explanation of Solution
Given:
The number of grape produced per acre is given by the function
Calculation:
The function of the number of grape produced per acre is given by
The standard form of function,
The maximum or minimum value of the function occurs at,
If
If
From the equation (1) and (2),
Substitute
The number of vines per acre is
The function has maximum value,
Substitute
The maximum grape production is
Thus, the number of vines that should be planted to maximize the grape production is
Chapter 3 Solutions
Precalculus: Mathematics for Calculus - 6th Edition