An apple farm yields an average of 34 bushels of apples per tree when 22 trees are planted on an acre of ground. Each time 1 more tree is planted per acre, the yield decreases by 1 bushel (bu) per tree as a result of crowding. How many trees should be planted on an acre in order to get the highest yield?
In order to get the highest yield, trees should be planted on an acre.
Answer
Final Answer: The number of trees that should be planted on an acre in order to get the highest yield is \(\boxed{39}\).
Step 1 ：The problem is asking for the maximum yield, which is the product of the number of trees and the yield per tree. This is a quadratic function, and the maximum value of a quadratic function occurs at its vertex.
Step 2 ：The formula for the x-coordinate of the vertex of a quadratic function \(y = ax^2 + bx + c\) is \(-b/2a\). In this case, \(a\) is -1 (the decrease in yield per tree for each additional tree), \(b\) is 34 (the initial yield per tree), and \(c\) is 22*34 (the initial total yield).
Step 3 ：So the x-coordinate of the vertex is \(-34/2*(-1) = 17\). However, this is the change in the number of trees, so the actual number of trees that gives the maximum yield is \(22 + 17 = 39\).
Step 4 ：Final Answer: The number of trees that should be planted on an acre in order to get the highest yield is \(\boxed{39}\).
