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 \(\boxed{39}\).