The DA office in Bradford PA specializes in two types of cases: mindless$-$fights $($M$)$ and roadrage $($R$)$; and earns $$2,500$ per M and $$4,000$ per $R.$ The DA works $48$ hours$/$week and the DA employs $S$ for $35$ hours$/$week & $L$ for $42$ hours$/$week$.$ M cases take up $6$ hours of the DA's time, $6$ hours of the $L\text{'}$s time and $3\mathrm{.}5$ hours of $S\text{'}$s time. R cases take $8$ hours of the DA's time, $3$ hours of $L\text{'}$s time and $7$ hours of $S^{\text{'}}s$ time. Derive the optimal M$-$R case mix to maximize DA's profits.

a$.$ Set up the objective function correctly

b$.$ Correctly set$-$up the constraints in the inequality and equality forms

$\backslash$table$[[$Constraints in inequality form,Constraints in equality form with slack variables$],[,],[,],[,]]$

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