Question

The table shows a company’s profit based on the number of pounds of food produced.

Answer 1

The answer is B 5,300

Answer 2

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,

$y=A+Bx+Cx^2$  

Where,

$A=\overline{y}-B\overline{x}-C(\overline{x})^2$

$B=\frac{S_{xy} S_{x^2x^2}-S_{x^2y}S_{xx^2}}{S_{xx}.S_{x^2x^2}-(S_{xx^2})^2}$

$C=\frac{S_{x^2y}.S_{xx}-S_{xy}S_{xx^2}}{S_{xx}S_{x^2x^2}-(S_{xx})^2}$

Also,

$S_{xx}=\frac{\sum(x_i-\bar{x})^2}{n}$

$S{xy}=\frac{(x_i-\bar{x})(y_i-\bar{y})}{n}$

$S_{xx^2}=\frac{\sum(x_i-\bra{x})(x_i^2-\bar{x^2})}{n}$

$S_{x^2x^2}=\frac{\sum(x_i-\bar{x^2})^2}{n}$

$S_{x^2y}=\frac{\sum (x_i^2-\bar{x^2})(y_i-\bar{y})}{n}$

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,

$y=-20420.96+102.24x-0.082x^2$

For x = 350 pounds,

$y=-20420.96+102.24(350)-0.082(350)^2$

$=5318.04$

Which is nearby 5300,

Hence, option B is correct.