There are 50 apple trees in an orchard. Each tree produces 800 appples. For each additional tree planted in the orchard, the output per tree doprs by 10 apples. How many trees should be added to the existing orchard in order to maximize the total output of trees?

I don't understand what it means to maximize the total output of trees. How am I supposed to do that?

Question

There are 50 apple trees in an orchard. Each tree produces 800 appples. For each additional tree planted in the orchard, the output per tree doprs by 10 apples. How many trees should be added to the existing orchard in order to maximize the total output of trees?

I don't understand what it means to maximize the total output of trees. How am I supposed to do that?

anonymous · Answer

make up a nice quadratic equation with negative leading coefficient, and find the vertex. that will be give you the maximum

anonymous · Answer

:(

anonymous · Answer

ok lets go slow
at 50 trees there are $50\times 800=40,000$ apples
how about if there are 51 trees?

anonymous · Answer

well there are 51 trees, but now each produces only $800-10=790$ apples
so we get a total of $51\times 790=40,290$ an increase for sure

anonymous · Answer

only one more
suppose there are $52$ trees, each one produces $800-20=780$ apples for a total of $52\times 780=40,560$

now lets cut to the chase

anonymous · Answer

suppose you add $x$ trees. 
then you have a total of $50+x$ trees, and they each produce $800-10x$ apples for a total of 
$$(50+x)(800-10x)$$ apples
there is your quadratic function, multiply out, find the vertex, and that will be your answer

anonymous · Answer

let me know if you need any help with that

anonymous · Answer

How did you get 10x?

anonymous · Answer

Nevermind. Thanks!

anonymous · Answer

yw