LP model formulation $(30$ pts$)$

a$.(10$ pts$)$ Define the decision variables, objective, and constraints for this LP problem.

b$.(10$ pts$)$ Write down the LP objective function in terms of the decision variables $($i$.$e$.,$ in a mathematical expression$)$

c$.(10$ pts$)$ Write out the constraints in terms of the decision variables $($i$.$e$.,$ in mathematical expressions$)$

The Outdoor Furniture Corporation manufactures

two products, benches and picnic tables, for use in yards and parks.

The firm has two main resources: its carpenters $($labor force$)$ and

a supply of redwood for use in furniture. During the next produc$-$

tion cycle, $1,200$ hours of labor are available under a union agree$-$

ment. The firm also has a stock of $3,500$ board feet of quality

redwood. Each bench that Outdoor Furniture produces requires

$4$ labor$-$hours and $10$ board feet of redwood; each picnic table

takes $6$ labor$-$hours and $35$ board feet of redwood. Completed

benches will yield a profit of $$9$ each, and tables will result in a

profit of $$20$ each. How many benches and tables should opera$-$

tions manager Shilei Yang produce in order to obtain the largest

possible profit?