PDC produces four different types of wood panels: Shiplap, Tongue and Groove, Board and Batten, and Beadboard. Each type of paneling is made by gluing and pressing together a different mixture of pine and oak chips. The following table summarizes the required amount of gluing, pressing, and the mixture of wood chips required to produce a pallet of $50$ units of each type of paneling:

$\backslash$table$[[$Resources Required per Pallet of Paneling Type$],[,$Shiplap,Tongue and Groove,Board and Batten,Beadboard$],[$Glue $($quarts$),50,50,100,50],[$Pressing $($hours$),5,15,10,5],[$Pine chips $($pounds$),500,400,300,200],[$Oak chips $($pounds$),500,750,250,500]]$

In the next 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 Shiplap, Tongue and Groove, Board and Batten, and Beadboard panels can be sold for profits of $$450,$$$1,150,$$$800,$ and $$400,$ respectively.

Question: PDC needs your assistance in figuring out how many of each type of paneling need to be manufactured to maximize the profit? Hint: Given the information above, use Solver to assist PDC in this optimization decision$-$making analysis.