Answer:
B) 5,300
Step-by-step explanation:
Let x represents the pounds of food produced and y represents the profit in dollars,
Thus, the table that shows the given situation would be,
x 100 250 500 650 800
y -11000 0 10300 11500 9075
Since, the equation of a quadratic equation is,
[tex]y=A+Bx+Cx^2[/tex]
Where,
[tex]A=\overline{y}-B\overline{x}-C(\overline{x})^2[/tex]
[tex]B=\frac{S_{xy} S_{x^2x^2}-S_{x^2y}S_{xx^2}}{S_{xx}.S_{x^2x^2}-(S_{xx^2})^2}[/tex]
[tex]C=\frac{S_{x^2y}.S_{xx}-S_{xy}S_{xx^2}}{S_{xx}S_{x^2x^2}-(S_{xx})^2}[/tex]
Also,
[tex]S_{xx}=\frac{\sum(x_i-\bar{x})^2}{n}[/tex]
[tex]S{xy}=\frac{(x_i-\bar{x})(y_i-\bar{y})}{n}[/tex]
[tex]S_{xx^2}=\frac{\sum(x_i-\bra{x})(x_i^2-\bar{x^2})}{n}[/tex]
[tex]S_{x^2x^2}=\frac{\sum(x_i-\bar{x^2})^2}{n}[/tex]
[tex]S_{x^2y}=\frac{\sum (x_i^2-\bar{x^2})(y_i-\bar{y})}{n}[/tex]
By substituting the values,
We get,
A ≈ -20420.96
B ≈ 102.24
C ≈ -0.082
Hence, the quadratic equation that shows the given situation is,
[tex]y=-20420.96+102.24x-0.082x^2[/tex]
For x = 350 pounds,
[tex]y=-20420.96+102.24(350)-0.082(350)^2[/tex]
[tex]=5318.04[/tex]
Which is nearby 5300,
Hence, option B is correct.
