The Lagrangian for this function and the given constraints is

which has partial derivatives (set equal to 0) satisfying

This is a fairly standard linear system. Solving yields Lagrange multipliers of

and

, and at the same time we find only one critical point at

.
Check the Hessian for

, given by


is positive definite, since

for any vector

, which means

attains a minimum value of

at

. There is no maximum over the given constraints.
Odd.................................
The equation of the least-squared regression line is: In(Element) = 2.305 - 0.101(Time).
<h3>What is a regression line?</h3>
A regression line displays the connection between scattered data points in any set. It shows the relation between the dependent y variable and independent x variables when there is a linear pattern.
According to the given problem,
From the table we can see,
ln(Element) is the dependent variable and Time is the independent variable.
The constant = 2.305,
Time = -0.101
Hence, we can conclude, our least squared regression line will be
In (Element) = 2.305 - 0.101 (Time).
Learn more about regression line here: brainly.com/question/7656407
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The answer to this problem would be B because your going up by 6