P$2)$ Consider the same project specified in $P1$ that requires $4800m^3$ of sand, $5800m^3$ of

fine gravel and $5700m^3$ of coarse gravel. You are now informed that two of the pits $($Pit $3$

and Pit $4)$ are out of commission due to safety violations, and you now have to get all your

material from Pits $1$ and $2.$

$($a$)$ Model the problem as a linear system of equations and write it in terms of

$[A]\{x\}=\{B\}$

$($b$)$ Determine the volume of material that needs to be acquired from each of the two

pits to meet the project requirements using pseudo$-$inverses by hand $($you are not

allowed to use MATLAB$).$

$($c$)$ Has the solution truly met the requirements of the project? If it has, is this solution

unique? If it has not, why not?

$($d$)$ What is the solution you get by using $\frac{A}{\frac{?}{?}}B$ in MATLAB? Does this solution truly meet

the requirements of the project? If it is different from the solution obtained in $($b$),$

explain how this possible? Submit screenshots of command window