Wick Industries makes and sells two products, X$1$ and X$2.$ The unit contribution margin of X$1$ is $$6,$ and the unit contribution margin of X$2$ is $$24.$

The production process for both products requires processing time in Departments A and B$.$ Each unit of X$1$ requires $12$ labor hours in Department A and $4$ labor hours in Department B$.$ Each unit of X$2$ requires $6$ labor hours in Department A and $8$ labor hours in Department B$.$

There are $360$ labor hours available in Department A and $240$ hours available in Department B$.$

a$.$ Using Solver, what product mix will maximize total contribution?

b$.$ Using Solver, solve the dual linear program for the linear program you solved in part a$.$

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