The fruit yield per tree in an orchard that contains 50 trees is 100 pounds per tree each year. Due to crowding, the yield decreases by 1 pounds per season per every additional tree planted. How many additional trees should be planted for a maximum total annual yield?
A)25 additional trees
B)50 additional trees
C)15 additional trees
D)75 additional trees
E)20 additional trees

Question

Quizplus · Accepted Answer

The total yield can be represented by the equation Y = (100 - (x-50)) * x, where x is the total number of trees. Differentiating this equation with respect to x and setting it to zero gives the maximum yield point. Solving this gives x = 75, which means 25 additional trees should be planted to achieve the maximum total annual yield.

The Fruit Yield Per Tree in an Orchard That Contains