Define the decision variables that will be needed to formulate a linear programming $($LP$)$ model for this problem.

$(10$ marks$)$

$($b$)$ Formulate the Linear Programming $($LP$)$ model that represents this problem. $(30$ marks$)$

$($c$)$ Solve the LP model using SOLVER.

$(20$ marks$)$

$($d$)$ Interpret your SOLVER solution within the context of the original business problem $(20$ marks$)$