Answer:
16428 oranges
Explanation:
Total yield = number of trees × number of oranges in each tree
Initial yield = 600×24= 14400 oranges
To find the equation needed, let x = additional trees and y= total yield
Number of trees = 24 +x
Number of oranges in each tree = 600-12x
Equation of total yield y= (24+x)(600-12x)
y= 14400-288x+600x-12x²
y= -12x²+312x+14400
Using a graphing calculator, from the graph drawn for this quadratic equation, we notice that it is a parabola. Therefore to find the maximum value, we should find the maximum point which is at the vertex of the parabola, we use the formula x= -b/2a
A quadratic equation is such: ax²+bx+c
Therefore x =-312/2×-12
x= -312/-24
x= 13
So we can conclude that in order to maximise oranges from the trees, the person needs to plant an additional 13 trees. Substituting from the above:
24+x=24+13= 37 trees in total
y= -12x²+312x+14400= -12×13²+312×13+14400= -2028+4056+14400
=16428 oranges in total yield
The number of trees that gives the most yield is 37
The given parameters are:
Represent the additional number of trees with x.
So, we have:
The equation that represents the total yield (y) becomes
[tex]y = (24 + x) \times (600 - 12x)[/tex]
Expand
[tex]y= 14400-288x+600x-12x\²[/tex]
Evaluate the like terms
[tex]y= 14400+312x-12x\²[/tex]
Rewrite as:
[tex]y= -12x\²+312x+14400[/tex]
Differentiate
[tex]y'= -24x+312[/tex]
Set to 0
[tex]-24x+312 = 0[/tex]
Solve for x
[tex]-24x=-312[/tex]
[tex]x=13[/tex]
Recall that:
Trees per acre = 24 + x
This gives
[tex]Trees = 24 + 13[/tex]
[tex]Trees = 37[/tex]
Hence, the number of trees that gives the most yield is 37
Read more about quadratic functions at:
https://brainly.com/question/11631534
