A peach orchard owner wants to maximize the amount of peaches produced by her orchard. She cannot simply plant as many trees as she can, since planting more trees will decrease the amount of fruit that each tree produces (the yield of each tree). She has found that the per-tree yield can be described by the equation Y = 850 - 25 x. Here Y is the yield per tree and x is the number of trees planted per acre. For example, if there were 10 trees planted per acre, each tree would produce 850 - 25 * 10 = 600 peaches. Find the number of trees per acre that should be planted in order to produce the maximum crop and the resulting total yield. Number of trees per acre : trees per acre Total yield : peaches per acre Give your first answer correct to two decimal places, and the second answer correct to the nearest peach per acre.
A peach orchard owner wants to maximize the amount of peaches produced by her orchard.
She cannot simply plant as many trees as she can, since planting more trees will decrease the amount of fruit that each tree produces (the yield of each tree).
She has found that the per-tree yield can be described by the equation
Y = 850 - 25 x.
Here Y is the yield per tree and x is the number of trees planted per acre.
For example, if there were 10 trees planted per acre, each tree would produce 850 - 25 * 10 = 600 peaches.
Find the number of trees per acre that should be planted in order to produce the maximum crop and the resulting total yield.
Number of trees per acre : trees per acre
Total yield : peaches per acre
Give your first answer correct to two decimal places, and the second answer correct to the nearest peach per acre.
Introduction:
Finding a parabola maximum value, The vertex (h, k) is indeed the lowest point on parabola if it opens up. The smallest functional or absolute minimum value of f is referred to as k. When x Equals h, this happens. k is the highest functional or absolute maximum value of f(x) when the parabola opens down, and it happens at x = h.
Given:
To find: Number of trees per acre.
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