Solve the following Linear Programming problem graphically, using the corner point method. Ensure that you label the constraints and feasible region clearly. Highlight the feasible region. Explicitly indicate the optimal solution and state the optimal solution in words.

Student Storage Lockers has some flexibility in how they configure their storage lockers for the year. They are trying to determine how much to make of each of the two sizes of lockers: Large $(L)$ and Small $($S$)$ The amount of resources and limits the amount of each size of storage locker units they can make. Its objective is to maximize profit.

$\backslash$table$[[$Maximize$,50$ L$,+,20$ S$,],[$Subject to$],[$Budget$,2$ LSquare Meters,Rental Limit $($large$),$LNon$-$negativity,,,S$,,>=,0]]$

$\backslash$table$[[$Co$-$ordinates $($L$,$S$),$Profit $($$$)],[(0,0),0],[,],[,],[,],[,]]$