Answer :
5 additional trees give maximum yield and 35 trees per acre will give largest crop of apple.
Let's assume that, we are planting x apple trees extra per acre. So, net 10x apple will be less.
Let say, total number of apples = y
Then, y = (30+x)×(400–10x)
For, optimum number of trees, let's do the differentiation of the above equation with respect to x.
d(y)/d(x) = (400–10x)×1 + (30+x)×(-10)
= 400–10x-300–10x
= 100–20x …………..(1)
For mimima or maxima, the above equation must be equal to 0.
So, 0 = 100–20x
=> x=5
Let's do the second differentiation of equation (1) and substitute the the value of x I.e x=5
[tex]d^2(y)/d(x^2) = -20[/tex]
The above equation is negative for all values of x which indicates that at x=5 we will have the maximum value.
So, the number of trees for maximum apple will be (30+x)
So, 30+5 = 35 trees per acre will give the largest crop of apple.
Hence 5 additional trees give maximum yield and 35 trees per acre will give largest crop of apple.
Learn more about maxima and minima at:
brainly.com/question/82347
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Final answer:
To find the total number of apples produced by 200 trees, convert the mass of apples per tree to grams, divide by the average mass of an apple, and multiply by the number of trees. Rounding the result gives us approximately 59000 apples.
Explanation:
To calculate the total number of apples produced by 200 trees, with each tree producing 48.5 kg of apples and each apple weighing an average of 165 g, we first need to convert the mass of apples per tree into grams and then divide by the average mass of one apple.
- Step 1: Convert kg to g for each tree's apple production:
48.5 kg/tree × 1000 g/kg = 48500 g/tree
- Step 2: Calculate the number of apples per tree:
48500 g/tree ÷ 165 g/apple = 293.9394 apples/tree (approximately)
- Step 3: Calculate the total number of apples for 200 trees:
293.9394 apples/tree × 200 trees = 58787.88 apples
Finally, rounding to the nearest thousand, we get a total of 59000 apples produced by the 200 trees.
