A Florida citrus grower estimates that if 60 orange trees are planted, the average yield per tree will be 500 oranges. The average yield will decrease by 5 oranges per tree for each additional tree planted on the same acreage. How many trees should the grower plant to maximize the total yield?
A) 80 trees
B) 30 trees
C) 20 trees
D) 75 trees

Question

Quizplus · Accepted Answer

The total yield can be represented by the equation Y = (500 - 5(x - 60))x, where x is the number of trees. Differentiating this equation with respect to x and setting the derivative equal to zero gives the number of trees that maximizes the yield. Solving this optimization problem, we find that planting 80 trees maximizes the total yield.

A Florida Citrus Grower Estimates That If 60 Orange Trees