A Florida citrus grower estimates that if 150 orange trees are planted, each tree will produce 500 oranges. For each additional tree planted on the same acreage, the number of oranges each tree produces will decrease by 10 oranges. Find the maximum number of oranges the citrus grower can produce. How many trees will the citrus grower need to plant?

The answer is below

Step-by-step explanation:

The question would not give a valid answer, the question should be in the form:

A Florida citrus grower estimates that if 30 orange trees are planted, each tree will produce 500 oranges. For each additional tree planted on the same acreage, the number of oranges each tree produces will decrease by 10 oranges. Find the maximum number of oranges the citrus grower can produce. How many trees will the citrus grower need to plant?

Solution:

Let x represent the number of orange trees above 30 to be planted on the acreage and let y be the number of oranges. Since for every additional tree there is a decrease of 10 oranges, hence:

y = (30 + x)(500 - 10x)

y = 15000 - 300x + 500x - 10x²

y = 15000 + 200x - 10x²

The number of oranges is maximum at y' = 0. Hence:

y' = 200 - 20x

200 - 20x = 0

20x = 200

x = 10

Second derivative test = y" = -20 (so this is maximal)

Therefore the number of trees needed = 30 + 10 = 40 trees

Maximum number of oranges = (30 + 10)(500 - 10(10)) = 40(400) = 16000 oranges

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step-by-step explanation:

to plot points   for x just start at the origin (middle) and go to the left however many times it say(if the number is a positive) if the number is a negative then go right however many times it says if it is 0 go nowhere

now keep you pencil there and go up however many times it says on y(if it is positive) if it is negative then go down however many times it says. if it says 0 go nowhere.

you have just plotted a point! now when you finish plotting all of them connect them with a ruler

plot each point as (-3, 7), (0,4), (3,1), (8,-4)   in the parenthesis on the left of the comma is x and the right is y.