The farmer should plant 40 trees per acre to maximize her yield to harvest.
A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
Let F be the number of fruit per acre
[tex]F = (70 + x) \times (30 - 3x) \\F = 70 \times 30 - 70 \times 3x + 30 \times x - 3x^2 \\F = 2100 - 210 x + 30x - 3x^2 \\F = 2100 - 180x - 3x^2[/tex]
Factor out the 3 and complete the square
[tex]F = -3x^2 - 180x + 2100\\F = -3 \times (x^2 + 60x - 700) \\F = -3 \times (x^2 + 2 * 30x + 30^2 - 30^2 - 700) \\F = -3 \times ((x + 30)^2 - 500 - 900) \\F = -3 \times ((x + 30)^2 - 400) \\F = -3 \times (x + 30)^2 + 1200\\[/tex]
So the vertex is at (-30, 1200)
70 - 30 = 40
The farmer should plant 40 trees per acre to maximize her yield to harvest.
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