How many trees will maximize the yield?

Question

The yield in bushels from a grove of orange trees is given Y=x(800-x), where x is the number of orange trees per acre.

Answer 1

Your function can be rewritten as y=-x^2 + 800x.

 

The maximum or minimum value of a parabola is always on the axis of symmetry which has the general equation of

x=-b/2a

 

In your case, the axis of symmetry is x = -800/-2 or x=400.

 

This means that planting 400 trees will maximize your yield. If you plug in x=400 into your function, you will find that your maximum yield will be y=400(800-400) = 160000.

 

You can sort of check this by plugging in 399 and 401 and see if the yield is less than 160000, so I'll do that.

y=399(800-399)=399(401) = 159999

y=401(800-401)=401(399) = 159999

 

Hope this helps.