At present 40 apple trees are planted per acre and the average yield is 20 bushels per tree. Suppose the experienced grower estimates that for every 5 new trees added per acre, the yield will decrease by 2 bushels per tree. One is interested in how many trees should be planted per harvest.
Let x=trees per acre added
Let H(x)=bushels of apples per acre.
I know that there should be 45 trees/acre for the max bushels, but how do I get the equation? Any help would be appreciated.
2007-10-28 13:01:59 · 3 answers · asked by Liz 4 in Science & Mathematics ➔ Mathematics
Yopu need to plant all that are required. Since the yeild will decrease by 2 bushels for every 5 trees planted, that means for every 100 trees planted you will pull 1 bushel out your wazzoo. Doesn't seem like you will be in business very long at this rate.pp
2007-10-28 13:14:10 · answer #1 · answered by ttpawpaw 7 · 0⤊ 0⤋
Using the variables that you established....
H(x) = (trees/acre) * (bushels/tree)
= [40 + x]*[20 - (2x/5)]
= 800 + 4x - 0.4x^2
To find out what value of x maximizes H(x), find the first derivative and set it equal to 0....
H'(x) = 4 - 0.8x = 0
0.8x = 4 --------------> x = 5 trees/acre should be added
The grower should have 45 trees/acre planted to achieve the best harvest.
2007-10-28 14:06:48 · answer #2 · answered by The K-Factor 3 · 0⤊ 0⤋
it is an up-beginning parabola. enable the vertex (the place the twine touches the line) be (0, 0). Then the tops of the towers are (-ninety, 80) and (ninety, 80). because of the fact the vertex is (0, 0), this variety of the equation simplifies to ?y = ax² Use the coordinates of the properly-known factors to confirm a. 80 = a90² a = 80/ninety² = 2/2025 The equation will become ?y = (2/2025)x²
2016-11-09 19:11:45 · answer #3 · answered by Anonymous · 0⤊ 0⤋