Let \[ A = \begin{bmatrix} 1 & 1 & 1 \\ 1 & 3 & 1 \\ -2 & -3 & -3 \end{bmatrix}, \quad b = \begin{bmatrix} b_1 \\ b_2 \\ b_3 \end{bmatrix}. \] For \( Ax = b \) to be solvable, which one of the following options is the correct condition on \( b_1, b_2, \) and \( b_3 \)?
The annual profit of a company depends on its annual marketing expenditure. The information of preceding 3 years' annual profit and marketing expenditure is given in the table. Based on linear regression, the estimated profit (in units) of the 4superscript{th year at a marketing expenditure of 5 units is ............ (Rounded off to two decimal places)} 
Which model is represented by the following graph?

The following graph represents:
A carpenter needs to make a wooden cuboidal box, closed from all sides, which has a square base and fixed volume. Since he is short of the paint required to paint the box on completion, he wants the surface area to be minimum.
On the basis of the above information, answer the following questions :
Find \( \frac{dS}{dx} \).
