Solve.
-The effective yield from a grove of miniature pear trees is described by the equation $\mathrm { E } = x ( 800 - x )$, where $x$ is the number of pear trees per acre. What is the maximum effective yield? How many pear trees per acre should be planted to achieve the maximum yield?
A) Maximum yield $= 160,000$
number of trees per acre planted $= 800$
B) Maximum yield $= 160,000$
number of trees per acre planted $= 400$
C) Maximum yield $= 160,000$
number of trees per acre planted $= 200$
D) Maximum yield $= 40,000$
number of trees per acre planted $= 200$

Question

Solve.
-The effective yield from a grove of miniature pear trees is described by the equation $\mathrm { E } = x ( 800 - x )$, where $x$ is the number of pear trees per acre. What is the maximum effective yield? How many pear trees per acre should be planted to achieve the maximum yield?
A) Maximum yield $= 160,000$
number of trees per acre planted $= 800$
B) Maximum yield $= 160,000$
 number of trees per acre planted $= 400$
C) Maximum yield $= 160,000$
number of trees per acre planted $= 200$
D) Maximum yield $= 40,000$
number of trees per acre planted $= 200$

Quizplus · Accepted Answer

The equation $E = x(800 - x)$ is a quadratic equation that opens downwards (since the coefficient of $x^2$ is negative), which means it has a maximum value at its vertex. The x-coordinate of the vertex of a parabola given by $ax^2 + bx + c$ is $-\frac{b}{2a}$. In this case, $a = -1$ and $b = 800$, so the x-coordinate is $-\frac{800}{2(-1)} = 400$. Plugging $x = 400$ back into the equation gives the maximum yield $E = 400(800 - 400) = 400 \times 400 = 160,000$.

Solve -The Effective Yield from a Grove of Miniature Pear E=x(800−x)\mathrm { E } = x ( 800 - x )E=x(800−x)

Solve
-The Effective Yield from a Grove of Miniature Pear $\mathrm { E } = x ( 800 - x )$