the question is in my description, it would not fit

Question

An apple orchard has an average yield of 36 bushels of apples/tree if tree density is 22 trees/acre. For each unit increase in tree density, the yield decreases by 2 bushels/tree. How many trees should be planted to maximixe the yield?

Answer 1

You can find the yield per acre for the orchard by multiplying the apple production per tree times the tree density per acre. If you add x to the density, you must subtract 2x from the yield.

 

Y = (36-2x)*(22+x)

 

You'll want to multiply this together and then find the vertex of this parabola. The x² term is negative, so it opens downward, which makes the vertex the maximum.

 

If you've done derivatives, take the first derivative, and set it equal to 0 to find the value of x that maximizes Y. You should then plant (22+x) trees/acre.

 

I hope this helps, please comment if you have further questions!