A home gardener estimates that 16 apple trees will have an average yield of 80 apples per tree. But because of the size of the garden, for each additional tree planted the yield will decrease by four apples per tree. How many trees should be planted to ma

The optimal number of trees to plant can be found by using calculus. Let x be the number of additional trees planted. Then the yield of apples for each tree is given by 80-4x. Thus, the total yield of apples is 16(80) + (80-4x)x = 1280 - 4x^2. To find the maximum yield, we take the derivative of the total yield with respect to x, set it equal to zero, and solve for x: d(1280 - 4x^2)/dx = -8x -8x = 0 x = 0 Therefore, the optimal number of additional trees to plant is 0, which means that the gardener should only plant the original 16 trees. The maximum yield of apples is 16(80) = 1280.