Problem $1$: Burger Office Equipment produces two types of desks, standard and deluxe, Deluxe desks oak tops and more expensive hardware and require additional time for finishing and polishing. Stan desks require $70$ board feet of pine and $10$ hours of labor, whereas deluxe desks require $60$ board fee pine, $18$ square feet of oak, and $15$ hours of labor. For the next week, the company has $5,000$ board $f$ of pine, $750$ square feet of oak, and $400$ hours of labor available. Each standard desk costs $$200$ and s for $$425.$ Each deluxe desk costs $$250$ and sells for $$570.$ All desks can be sold to national chains such Staples or Office Depot.

a$.$ Identify the decision variables in simple verbal statements.

b$.$ Mathematically formulate a linear optimization model.

c$.$ Sketch the feasible region.

d$.$ Find the optimal solution and objective value.

e$.$ Identify any redundant constraints in this model.