$1$ Simplex Method $-25$ Pts

Imagine that you manage a factory that produces four different types of wood paneling. Each type of

paneling is made by gluing and pres$$ing together a different mixture of pine and oak chips. The follow$-$

ing table summarizes the required amount of gluing, pressing, and mixture of wood chips required to

produce a pallet of each type of paneling. The table shows the resource required per pallet of paneling

type.

In each production cycle, you have $5,800$ quarts of glue; $730$ hours of pressing capacity; $29,200$

pounds of pine chips; and $60,500$ pounds of oak chips available. Further assume that each pallet of

Tahoe, Pacific, Savannah, and Aspen panels can be sold for profits of $$450,$$$1,150,$$$800,$ and $$400,$

respectively:

Maximize the profit with the given constraints using Simplex Method. Ignore the computation of

slack and surplus variables,

a$.)(10$ points$)$ Construct the linear programming problem.

b$.)($I$5$ points$)$ Compute for the maximum profit using matrix manipulation in Simplex Method.