Acommercial cherry grower estimates from past records that if 20 trees are planted per acre, then each tree will yield an average of 36 pounds of cherries per season. if, for each additional tree planted per acre (up to 25), the average yield per tree is reduced by 1 pound, how many trees should be planted per acre to obtain the maximum yield per acre? what is the maximum yield?

Step-by-step explanation:

If x is the number of trees planted per acre, we are told the yield per tree is ...

  36 -(x -20) = 56 -x . . . lbs

The total yield per acre is the product of the number of trees and the yield per tree:

  y = x(56 -x)

This function describes a parabolic curve with zeros at x=0 and x=56. The curve opens downward, so will have its peak value halfway between these zeros, at x = (0 +56)/2 = 28.

28 tree per acre should be planted to maximize yield.

That yield will be (28)(56 -28) = 784 pounds per acre.

_____

Additional comment

We have to assume that the remark "up to 25" refers to additional trees per acre, rather than the total number of trees per acre.

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

hello from mrbilldoesmath!

answer:

25x^2 + 90x + 84

discussion:

mn(x) = m(n(x)) = m( 5x + 9) =

(5x + 9)^2 + 3 =>

25x^2 + 90x + 9^2 + 3 =

25x^2 + 90x + 84                 (as 9^2 = 9*9 = 81)

which is the second choice

regards,  

mrb

p.s.   i'll be on vacation from friday, dec 22 to jan 2, 2019. have a great new year!