Optimization Calculus Problem. I got 34, not sure if its right.

Question

The owner of an orange grove estimates that if 14 trees are planter per acre, then each mature tree will yield 600 oranges per year. For each additional tree planted per acre, the number of oranges produces by each year decrease by 12 per year. How many trees should be planted per acre to obtain the most oranges per year?

Answer 1

Let x = number of additional trees to plant

Let f(x) = total yield of oranges per year if x additional trees are planted

f(x) = (yield per tree)(number of trees) = (600 - 12x)(x + 14)

The graph of y = f(x) is a parabola opening downward with x-intercepts -14 and 50. The maximum occurs for the value of x that is halfway between the x-intercepts (i.e., when x = 18).

So, to maximize yield, plant 18 additional trees. That is, plant 14+18 = 32 trees.