Question

2.) answer the following and provide a written response. 2 points the amount s (in pounds per acre) of sugar produced from sugar beets can be modeled by the function: s = - 0.0655n² + 7.855n + 5562 where n is the amount (in pounds per acre) of nitrogen fertilizer used. how much fertilizer should you use to maximize sugar production? what is the maximum amount of sugar you can produce?

Explanation:

Step1: Find n for max s (vertex)

$n = -\frac{b}{2a} = -\frac{7.855}{2(-0.0655)} \approx 60$

Step2: Calculate max s with n=60

$s = -0.0655(60)^2 + 7.855(60) + 5562 \approx 5797.5$

Answer:

Use 60 pounds per acre of fertilizer to maximize sugar production, with a maximum of 5797.5 pounds per acre.